Thèses : « Statistica bivariata »

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Onnen, Nathaniel J. « Estimation of Bivariate Spatial Data ». The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1616243660473062.

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Casanova, Gurrera María de los Desamparados. « Construction of Bivariate Distributions and Statistical Dependence Operations ». Doctoral thesis, Universitat de Barcelona, 2005. http://hdl.handle.net/10803/1555.

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Dependence between random variables is studied at various levels in the first part, while the last two chapters are devoted to the construction of bivariate distributions via principal components. Chapter 1 of Preliminaries is devoted to general dependence concepts (Fréchet classes, copulas, and parametric families of distributions). In Chapter 2, we generalize the union and intersection operations of two distance matrices to symmetric nonnegative definite matrices. These operations are shown to be useful in the geometric interpretation of Related Metric Scaling (RMS ), and possibly in other approaches of Multivariate Analysis. They show relevant properties that are studied in this chapter. The behaviour of the operations is, in some way, analogous to that presented by the intersection and union between vector spaces; in particular, we prove that the intersection of orthogonal matrices is the null matrix, while the union is the direct sum of the matrices. Matrices that share their eigenvectors form an equivalence class, and a partial order relation is defined. This class is closed for the union and intersection operations. A continuous extension of these operations is presented in Chapter 3. Infinite matrices are studied in the context of bounded integral operators and numerical kernels. We put the basis for extending RMS to continuous random variables and, hence, infinite matrices. The starting point is Mercer's Theorem, which ensures the existence of an orthogonal expansion of the covariance kernel K (s, t) = min {F (s) , F (t)} - F (s) F (t), where F is the cumulative distribution function of each marginal variable. The sets of eigenvalues and eigenfunctions of K, whose existence is ensured by the cited theorem, allow us to define a product between symmetric and positive (semi)definite kernels, and, further, to define the intersection and the union between them. Results obtained in the discrete instance are extended in this chapter to continuous variables, with examples. Such covariance kernels (symmetric and positive definite) are associated with symmetric and positive quadrant dependent (PQD) bivariate distributions. Covariance between functions of bounded variation defined on the range of some random variables, joined by distributions of this type, can be computed by means of their cumulative distribution functions. In Chapter 4, further consequences are obtained, especially some relevant relations between the covariance and the Fréchet bounds, with a number of results that can be useful in the characterization of independence as well as in testing goodness-of-fit. The intersection of two kernels (defined in Chapter 3) is a particular instance of the covariance between functions. Covariance is a quasiinner product defined through the joint distribution of the variables involved. A measure of affinity between functions with respect to H is defined, and also studied. In Chapter 5, from the concept of affinity between functions via an extension of the covariance, we define the dimension of a distribution, we relate it to the diagonal expansion and find the dimension for some parametric families. Diagonal expansions of bivariate distributions (Lancaster) allows us to construct bivariate distributions. It has proved to be adequate for constructing Markov processes, and has also been applied to engineering problems among other uses. This method has been generalized using the principal dimensions of each marginal variable that are, by construction, canonical variables. We introduce in Chapter 6 the theoretical foundations of this method. In Chapter 7 we study the bivariate, symmetric families obtained when the marginals are Uniform on (0, 1), Exponential with mean 1, standard Logistic, and Pareto (3,1). Conditions for the bivariate density, first canonical correlation and maximum correlation of each family of densities are given in some cases. The corresponding copulas are obtained.
Al Capítol 1 de Preliminars es revisen conceptes de dependència generals (classes de Fréchet, còpules, i famílies paramètriques de distribucions). Al Capítol 2, generalitzem les operacions unió i intersecció de dues matrius de distàncies a matrius simètriques semidefinides positives qualssevol. Aquestes operacions s'han mostrat d'utilitat en la interpretació geomètrica del Related Metric Scaling (RMS), i possiblement en altres tècniques d'Anàlisi Multivariant. S'estudien llur propietats que són similars, en alguns aspectes, a les de la unió i intersecció de subespais vectorials. Al Capítol 3 es presenta una extensió al continuu d'aquestes operacions, mitjançant matrius infinites en el context dels operadors integrals acotats i nuclis numèrics. S'estableix la base per a extendre el RMS a variables contínues i, per tant, a matrius infinites. Es parteix del Teorema de Mercer el qual assegura l'existència d'una expansió ortogonal del nucli de la covariança K (s, t) = min {F (s), F (t)} - F (s) F (t), on F és la funció de distribució de cada variable marginal. Els conjunts de valors i funcions pròpies d'aquest nucli ens permeten definir un producte entre nuclis i la intersecció i unió entre nuclis simètrics semidefinits positius. Tals nuclis de covariança s'associen amb distribucions bivariants també simètriques i amb dependència quadrant positiva (PQD). El producte de dos nuclis és un cas particular de covariança entre funcions, que es pot obtenir a partir de les distribucions conjunta i marginals, com s'estudia al Capítol 4 per a funcions de variació afitada, fixada la distribució bivariant H. S'obtenen interessants relacions amb les cotes de Fréchet. Aquesta covariança entre funcions és un producte quasiescalar a l'espai de funcions de variació afitada i permet definir una mesura d'afinitat. Al Capítol 5 aquesta H-afinitat s'utilitza per definir la dimensió d'una distribució. Les components principals d'una variable (Capítol 6) s'utilitzen com a variables canòniques a l'expansió diagonal de Lancaster (Capítol 7 i últim) per a construïr distribucions bivariants amb marginals Uniformes al (0,1), Exponencial de mitjana 1, Logística estàndard, i Pareto (3,1). S'obtenen condicions per la densitat bivariant, correlacions canòniques i correlació màxima per cada família. S'obtenen les còpules corresponents.

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Baggs, Maria Geraldine E. « Properties of order statistics from bivariate exponential distributions / ». The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487858417983938.

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Koen, Marthinus Christoffel. « The analysis of some bivariate astronomical time series ». Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/17341.

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Bibliography: pages 75-76.
In the first part of the thesis, a linear time domain transfer function is fitted to satellite observations of a variable galaxy, NGC5548. The transfer functions relate an input series (ultraviolet continuum flux) to an output series (emission line flux). The methodology for fitting transfer function is briefly described. The autocorrelation structure of the observations of NGC5548 in different electromagnetic spectral bands is investigated, and appropriate univariate autoregressive moving average models given. The results of extensive transfer function fitting using respectively the λ1337 and λ1350 continuum variations as input series, are presented. There is little evidence for a dead time in the response of the emission line variations which are presumed driven by the continuum. Part 2 of the thesis is devoted to the estimation of the lag between two irregularly spaced astronomical time series. Lag estimation methods which have been used in the astronomy literature are reviewed. Some problems are pointed out, particularly the influence of autocorrelation and non-stationarity of the series. If the two series can be modelled as random walks, both these problems can be dealt with efficiently. Maximum likelihood estimation of the random walk and measurement error variances, as well as the lag between the two series, is discussed. Large-sample properties of the estimators are derived. An efficient computational procedure for the likelihood which exploits the sparseness of the covariance matrix, is briefly described. Results are derived for two example data sets: the variations in the two gravitationally lensed images of a quasar, and brightness changes of the active galaxy NGC3783 in two different wavelengths. The thesis is concluded with a brief consideration of other analysis methods which appear interesting.

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He, Qinying. « Inference on correlation from incomplete bivariate samples ». Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1180468775.

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Wang, Chunnan. « Analysis of a new bivariate distribution in reliability theory ». Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/284128.

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Freund [1961] introduced a bivariate extension of the exponential distribution that provides a model in which the exponential residual lifetime of one component depends on the working status of another component. We define and study an extension of the Freund distribution in this dissertation. In the first chapter we define some basic concepts that are needed for later developments. We give the definition of the multivariate conditional hazard rate functions of a nonnegative absolutely continuous random vector and study a characterization of these functions in Section 1.1. Then we study some notions of aging: an increasing failure rate (IFR) distribution, a decreasing failure rate (DFR) distribution, an increasing failure rate average (IFRA) distribution, and a decreasing failure rate average (DFRA) distribution in Section 1.2. In Section 1.3 we study two concepts of multivariate dependence: association and positive quadrant dependence. In Chapter 2 we construct a shock model and the new bivariate distribution is the joint distribution of the resulting lifetimes. We explicitly compute the density function, survival function, moment generating function, marginal density functions and marginal survival functions. Also in this chapter, we study the correlation coefficient and other senses of positive dependence of the two random variables of the new bivariate distribution. Then we extend the new distribution to multivariate case. In Chapter 3 we study some aging properties. We obtain two results about the new distribution in n dimensions. The first result says that the marginal distributions of the new multivariate distribution have decreasing failure rate if the conditional hazard rates are decreasing and bounded above by 1. The second one concerns an (n-1 )-out-of-n system such that the joint distribution of the lifetimes of each component is the new distribution in n dimensions. It gives conditions on the parameters under which the system has an IFRA distribution. In Chapter 4 we develop some estimation procedure for the parameters a and b of the new bivariate distribution. We apply the method of moments and the maximum likelihood principle to estimate the parameters. We prove that the method of moments estimator is a consistent asymptotically normal estimator. Then we use Mathematica to run simulation and compare the method of moments estimator with the maximum likelihood estimator. We also compute the 95% confidence interval for a and b from the method of moments estimator. In the last chapter we study a stochastic ordering problem. We have two nonnegative n dimensional random vectors X and Y. We assume that X and Y have the same conditional hazard rates up to a certain level. We give a condition under which the two vectors X and Y are stochastically ordered.

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Murphy, Orla. « Copula-based tests of independence for bivariate discrete data ». Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=117229.

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New statistics are proposed for testing the hypothesis that two non-continuous random variables are independent. These statistics, which lead to consistent tests, are Cramér–von Mises and Kolmogorov–Smirnov type functionals of the checkerboard copula. The power of the new tests is compared via simulation to those based on the Pearson chi-squared, likelihood ratio, and Zelterman statistics often used in this context. To study their power, data are generated from five families of bivariate distributions whose margins may be known or not. In all cases considered, the new tests are seen to be more powerful than the standard tests. The new tests and the Zelterman statistic maintain their levels when the data are sparse; as is well known, this is not the case for Pearson's chi-squared and the likelihood ratio test. On the basis of the results presented here, the new Cramér–von Mises statistics can be recommended to test the independence between two random variables in the presence of ties in the sample.
De nouvelles statistiques sont proposées pour tester l'indépendance de deux aléas non continus. Ces statistiques, qui mènent à des tests convergents, sont des fonctionnelles de type Cramér–von Mises et Kolmogorov–Smirnov de la copule en damier. La puissance des nouveaux tests est comparée par simulation à celle des tests fondés sur les statistiques du khi-deux de Pearson, du rapport des vraisemblances et de la statistique de Zelterman souvent utilisées dans ce contexte. Pour étudier leur puissance, on génère des données de cinq familles de lois bivariées dont les marges peuvent être connues ou non. Dans tous les cas considérés, les nouveaux tests s'avèrent plus puissants que les tests standard. À l'instar du test de Zelterman, les nouveaux tests maintiennent leur seuil lorsque les données sont clairsemées; comme on le sait, ce n'est pas le cas des tests du khi-deux de Pearson et du rapport des vraisemblances. À la lumière des résultats présentés ici, les nouvelles statistiques de Cramér–von Mises peuvent être recommandées pour tester l'indépendance entre deux aléas en présence d'ex æquo dans les données.

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Lin, Min. « Correlation of Bivariate Frailty Models and a New Marginal Weibull Distribution for Correlated Bivariate Survival Data ». University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1307321226.

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Romeiro, Renata Guimarães 1987. « Modelo de regressão Birnbaum-Saunders bivariado ». [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307091.

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Orientador: Filidor Edilfonso Vilca Labra
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: O modelo de regressão Birnbaum-Saunders de Rieck e Nedelman (1991) tem sido amplamente discutido por vários autores, com aplicações na área de sobrevivência e confiabilidade. Neste trabalho, desenvolvemos um modelo de regressão Birnbaum-Saunders bivariado através do uso da distribuição Senh-Normal proposta por Rieck (1989). Este modelo de regressão pode ser utilizado para analisar logaritmos de tempos de vida de duas unidades correlacionadas, e gera marginais correspondentes aos modelos de regressão Birnbaum-Saunders univariados. Apresentamos um estudo de inferência e análise de diagnóstico para modelo de regressão Birnbaum-Saunders bivariado proposto. Em primeiro lugar, apresentamos os estimadores obtidos através do método dos momentos e de máxima verossimilhança, e a matriz de informação observada de Fisher. Além disso, discutimos testes de hipóteses com base na normalidade assintótica dos estimadores de máxima verossimilhança. Em segundo lugar, desenvolvemos um método de diagnóstico para o modelo de regressão Birnbaum- Saunders bivariado baseado na metodologia de Cook (1986). Finalmente, apresentamos alguns resultados de estudos de simulações e aplicações em dados reais
Abstract: The Birnbaum-Saunders regression model of Rieck and Nedelman (1991) has been extensively discussed by various authors with application in survival and reliability studies. In this work a bivariate Birnbaum-Saunders regression model is developed through the use of Sinh-Normal distribution proposed by Rieck (1989). This bivariate regression model can be used to analyze correlated log-time of two units, it bivariate regression model has its marginal as the Birnbaum- Saunders regression model. For the bivariate Birnbaum-Saunders regression model is discussed some of its properties, in the moment estimation, the maximum likelihood estimation and the observed Fisher information matrix. Hypothesis testing is performed by using the asymptotic normality of the maximum-likelihood estimators. Influence diagnostic methods are developed for this model based on the Cook¿s(1986) approach. Finally, the results of a simulation study as well as an application to a real data set are presented
Mestrado
Estatistica
Mestra em Estatística

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Zhao, Yanchun. « Comparison of Proposed K Sample Tests with Dietz's Test for Nondecreasing Ordered Alternatives for Bivariate Normal Data ». Thesis, North Dakota State University, 2011. https://hdl.handle.net/10365/28836.

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There are many situations in which researchers want to consider a set of response variables simultaneously rather than just one response variable. For instance, a possible example is when a researcher wishes to determine the effects of an exercise and diet program on both the cholesterol levels and the weights of obese subjects. Dietz (1989) proposed two multivariate generalizations of the Jonckheere test for ordered alternatives. In this study, we propose k-sample tests for nondecreasing ordered alternatives for bivariate normal data and compare their powers with Dietz's sum statistic. The proposed k-sample tests are based on transformations of bivariate data to univariate data. The transformations considered are the sum, maximum and minimum functions. The ideas for these transformations come from the Leconte, Moreau, and Lellouch (1994). After the underlying bivariate normal data are reduced to univariate data, the Jonckheere-Terpstra (JT) test (Terpstra, 1952 and Jonckheere, 1954) and the Modified Jonckheere-Terpstra (MJT) test (Tryon and Hettmansperger, 1973) are applied to the univariate data. A simulation study is conducted to compare the proposed tests with Dietz's test for k bivariate normal populations (k=3, 4, 5). A variety of sample sizes and various location shifts are considered in this study. Two different correlations are used for the bivariate normal distributions. The simulation results show that generally the Dietz test performs the best for the situations considered with the underlying bivariate normal distribution. The estimated powers of MJT sum and JT sum are often close with the MJT sum generally having a little higher power. The sum transformation was the best of the three transformations to use for bivariate normal data.

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Linder, Richard Scott. « Impact of censoring on sample variances and regression coefficient in a bivariate normal model / ». The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu148795190795651.

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Moodie, Felicity Zoe. « A new framework for nonparametric estimation of the bivariate survivor function / ». Thesis, Connect to this title online ; UW restricted, 2001. http://hdl.handle.net/1773/9535.

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Lee, Sukhoon. « Inference for a bivariate survival function induced through the environment / ». The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487267024997374.

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Blatchford, Patrick Judson. « Monitoring bivariate endpoints in group sequential clinical trials / ». Connect to full text via ProQuest. Limited to UCD Anschutz Medical Campus, 2007.

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Thesis (Ph.D. in Biostatistics) -- University of Colorado Denver, 2007.
Typescript. Includes bibliographical references (leaves 104-106). Free to UCD affiliates. Online version available via ProQuest Digital Dissertations;

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Ramos, Quispe Luz Marina 1985. « Uma extensão da distribuição Birnbaum-Saunders baseada na distribuição gaussiana inversa ». [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307087.

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Orientador: Filidor Edilfonso Vilca Labra
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Vários trabalhos têm sido feitos sobre a distribuição Birnbaum-Saunders (BS) univariada e suas extensões. A distribuição bivariada Birnbaum-Saunders (BS) foi apresentada apenas recentemente por Kundu et al. (2010) e algumas extensões já foram discutidas por Vilca et al. (2014) e Kundu et al. (2013). Eles propuseram uma distribuição BS bivariada com estrutura de dependência e estabeleceram várias propriedades atraentes. Este trabalho fornece extensões, univariada e bivariada, da distribuição BS. Estas extensões são baseadas na distribuição Gaussiana Inversa (IG) que é usada como uma distribuição de mistura no contexto de misturas de escala normal. As distribuições resultantes são distribuições absolutamente contínuas e muitas propriedades da distribuição BS são preservadas. Sob caso bivariado, as marginais e condicionais são do tipo Birnbaum-Saunders univariada. Para a obtenção da estimativa de máxima verossimilhança (EMV) é desenvolvido um algoritmo EM. Ilustramos os resultados obtidos com dados reais e simulados
Abstract: Several works have been done on the univariate Birnbaum-Saunders (BS) distribution and its extensions. The bivariate Birnbaum-Saunders (BS) distribution was presented only recently by Kundu et al. (2010) and some extensions have already been discussed by Vilca et al. (2014) and Kundu et al. (2013). They proposed a bivariate BS distribution with dependence structure and established several attractive properties. This work provides extensions, univariate and bivariate, of the BS distribution. These extensions are based on the Inverse Gaussian (IG) distribution that is used as a mixing distribution in the context of scale mixtures of normal. The resulting distributions are absolutely continuous distributions and many properties of the BS distribution are preserved. Under bivariate case, the marginals and conditionals are of type univariate Birnbaum-Saunders. For obtaining the maximum likelihood estimates (MLE) of the model parameters is developed an algorithm EM. We illustrate the obtained results with real and simulated dataset
Mestrado
Estatistica
Mestra em Estatística

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Lally, Kristine. « Assessing Relationships between Psychological and Biological Markers in Coronary Heart Disease Patients using Bivariate Linear Mixed Models ». Thesis, Uppsala universitet, Statistiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-326015.

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The Secondary Prevention in Uppsala Primary Health Care Project (SUPRIM) is a randomized controlled trial evaluating the effects of cognitive behavioral therapy on coronary heart disease patients. Various outcomes of psychological and physical health are recorded every six months approximately, over the course of two years after entry to the trial. In this thesis, relationships between the psychological outcome variables, Stress, Anxiety, Depression and Exhaustion, and five physical health biomarkers, are assessed using bivariate linear mixed models. Significant associations are found between one of the biomarkers and both Depression and Exhaustion, and also between one of the other biomarkers and Exhaustion.

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Beversdorf, Louanne Margaret. « Tests for Correlation on Bivariate Nonnormal Distributions ». UNF Digital Commons, 2008. http://digitalcommons.unf.edu/etd/284.

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Many samples in the real world are very small in size and often do not follow a normal distribution. Existing tests for correlation have restrictions on the distribution of data and sample sizes, therefore the current tests cannot be used in some real world situations. In this thesis, two tests are considered to test hypotheses about the population correlation coefficient. The tests are based on statistics transformed by a saddlepoint approximation and by Fisher's Z-transformation. The tests are conducted on small samples of bivariate nonnormal data and found to perfom well. Simulations were run in order to compare the type I error rates and power of the new test with other commonly used tests. The new tests controlled type I error rates well, and have reasonable power performance.

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Stewart, Jaimee E. « A Comparison of Methods for Generating Bivariate Non-normally Distributed Random Variables ». UNF Digital Commons, 2009. http://digitalcommons.unf.edu/etd/235.

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Many distributions of multivariate data in the real world follow a non-normal model with distributions being skewed and/or heavy tailed. In studies in which multivariate non-normal distributions are needed, it is important for simulations of those variables to provide data that is close to the desired parameters while also being fast and easy to perform. Three algorithms for generating multivariate non-normal distributions are reviewed for accuracy, speed and simplicity. They are the Fleishman Power Method, the Fifth-Order Polynomial Transformation Method, and the Generalized Lambda Distribution Method. Simulations were run in order to compare the three methods by how well they generate bivariate distributions with the desired means, variances, skewness, kurtoses, and correlation, simplicity of the algorithms, and how quickly the desired distributions were calculated.

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COLUMBU, SILVIA. « Parametric modeling of dependence of bivariate quantile regression residuals' signs ». Doctoral thesis, Università degli Studi di Cagliari, 2015. http://hdl.handle.net/11584/266587.

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In this thesis, we propose a non-parametric method to study the dependence of the quantiles of a multivariate response conditional on a set of covariates. We define a statistic that measures the conditional probability of concordance of the signs of the residuals of the conditional quantiles of each univariate response. The probability of concordance is bounded from below by the value of largest possible negative dependence and from above by that of largest possible positive dependence. The value corresponding to the case of independence is contained in the interior of that interval. We recommend two distinct regression methods to model the conditional probability of concordance. The first is a logistic regression with a logit link modified. The second one is a nonlinear regression method, where the outcome is modeled as a polynomial function of the linear predictor. Both are conceived to constrain the predicted probabilities to lie within the feasible range. The estimated probabilities can be tested against the values of largest possible dependence and independence. The method permits to capture important aspects of the dependence of multivariate responses and assess possible effects of covariates on such dependence. We use data on pulmonary disfunctions to illustrate the potential of the proposed method. We suggest also graphical tools for a correct interpretation of results.

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Strugnell, James Paul. « Paintings by numbers : applications of bivariate correlation and descriptive statistics to Russian avant-garde artwork ». Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/10722.

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In this thesis artwork is defined, through analogy with quantum mechanics, as the conjoining of the nonsimultaneously measurable momentum (waves) of artwork-text (words within the primary sources and exhibition catalogues) with the position (particles) of artwork-objects (artist- productivity/exhibition-quantities). Such a proposition allows for the changes within the artwork of the Russian avant-garde to be charted, as such artwork-objects are juxtaposed with different artwork-texts from 1902 to 2009. The artwork of an initial period from 1902 to 1934 is examined using primary-source artwork-text produced by Russian artists and critics in relation to the contemporaneous production-levels of various types of Russian-avant-garde artwork-objects. The primary sources in this dataset are those reproduced in the artwork-text produced by the 62 exhibitions described below, and those published in John E. Bowlt's 1991 edition of Russian Art of the Avant-Garde: Theory and Criticism. The production of artwork in the latter period from 1935 to 2009 is examined through consecutive exhibitions, and the relationship between the artwork-text produced by these exhibitions and the artwork-objects exhibited at them. The exhibitions examined within this thesis are 62 containing Russian avant-garde artwork, held in Britain from 1935 to 2009. Content analysis, using an indices-and-symptom analytical construct, functions to convert the textual, unstructured data of the artwork-text words to numerical, structured data of recording-unit weighted percentages. Whilst artist-productivity and exhibition-quantities of types of artwork-object convert the individual artwork-objects to structured data. Bivariate correlation, descriptive statistics, graphs and charts are used to define and compare relationships between: The recording units of the artwork-texts; the artist-productivity/ exhibition-quantities of types of artwork-objects; the structured artwork-text data and structured artwork-object data. These various correlations between structured artwork-text data and structured artwork-object data are calculated in relationship to time (Years) to chart the changes within these relationships. The changes within these relationships are synonymous with changes within Russian avant-garde artwork as presented from 1902 to 1934 and within the 62 British exhibitions from 1935 to 2009. Bivariate correlations between structured artwork-texts data and structured artwork-objects data express numerically (quantitatively) the ineffable relationships formed over time by large sets of unstructured data in the continued (re)creation of artwork.

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Jiang, Fan. « Application of a Bivariate Probit Model to Investigate the Intended Evacuation from Hurricane ». FIU Digital Commons, 2013. http://digitalcommons.fiu.edu/etd/883.

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With evidence of increasing hurricane risks in Georgia Coastal Area (GCA) and Virginia in the U.S. Southeast and elsewhere, understanding intended evacuation behavior is becoming more and more important for community planners. My research investigates intended evacuation behavior due to hurricane risks, a behavioral survey of the six counties in GCA under the direction of two social scientists with extensive experience in survey research related to citizen and household response to emergencies and disasters. Respondents gave answers whether they would evacuate under both voluntary and mandatory evacuation orders. Bivariate probit models are used to investigate the subjective belief structure of whether or not the respondents are concerned about the hurricane, and the intended probability of evacuating as a function of risk perception, and a lot of demographic and socioeconomic variables (e.g., gender, military, age, length of residence, owning vehicles).

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Kadel, Rajendra. « A Latent Mixture Approach to Modeling Zero-Inflated Bivariate Ordinal Data ». Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4701.

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Multivariate ordinal response data, such as severity of pain, degree of disability, and satisfaction with a healthcare provider, are prevalent in many areas of research including public health, biomedical, and social science research. Ignoring the multivariate features of the response variables, that is, by not taking the correlation between the errors across models into account, may lead to substantially biased estimates and inference. In addition, such multivariate ordinal outcomes frequently exhibit a high percentage of zeros (zero inflation) at the lower end of the ordinal scales, as compared to what is expected under a multivariate ordinal distribution. Thus, zero inflation coupled with the multivariate structure make it difficult to analyze such data and properly interpret the results. Methods that have been developed to address the zero-inflated data are limited to univariate-logit or univariate-probit model, and extension to bivariate (or multivariate) probit models has been very limited to date. In this research, a latent variable approach was used to develop a Mixture Bivariate Zero-Inflated Ordered Probit (MBZIOP) model. A Bayesian MCMC technique was used for parameter estimation. A simulation study was then conducted to compare the performances of the estimators of the proposed model with two existing models. The simulation study suggested that for data with at least a moderate proportion of zeros in bivariate responses, the proposed model performed better than the comparison models both in terms of lower bias and greater accuracy (RMSE). Finally, the proposed method was illustrated with a publicly-available drug-abuse dataset to identify highly probable predictors of: (i) being a user/nonuser of marijuana, cocaine, or both; and (ii), conditional on user status, the level of consumption of these drugs. The results from the analysis suggested that older individuals, smokers, and people with a prior criminal background have a higher risk of being a marijuana only user, or being the user of both drugs. However, cocaine only users were predicted on the basis of being younger and having been engaged in the criminal-justice system. Given that an individual is a user of marijuana only, or user of both drugs, age appears to have an inverse effect on the latent level of consumption of marijuana as well as cocaine. Similarly, given that a respondent is a user of cocaine only, all covariates--age, involvement in criminal activities, and being of black race--are strong predictors of the level of cocaine consumption. The finding of older age being associated with higher drug consumption may represent a survival bias whereby previous younger users with high consumption may have been at elevated risk of premature mortality. Finally, the analysis indicated that blacks are likely to use less marijuana, but have a higher latent level of cocaine given that they are user of both drugs.

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Li, Han. « Statistical Modeling and Analysis of Bivariate Spatial-Temporal Data with the Application to Stream Temperature Study ». Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/70862.

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Water temperature is a critical factor for the quality and biological condition of streams. Among various factors affecting stream water temperature, air temperature is one of the most important factors related to water temperature. To appropriately quantify the relationship between water and air temperatures over a large geographic region, it is important to accommodate the spatial and temporal information of the steam temperature. In this dissertation, I devote effort to several statistical modeling techniques for analyzing bivariate spatial-temporal data in a stream temperature study. In the first part, I focus our analysis on the individual stream. A time varying coefficient model (VCM) is used to study the relationship between air temperature and water temperature for each stream. The time varying coefficient model enables dynamic modeling of the relationship, and therefore can be used to enhance the understanding of water and air temperature relationships. The proposed model is applied to 10 streams in Maryland, West Virginia, Virginia, North Carolina and Georgia using daily maximum temperatures. The VCM approach increases the prediction accuracy by more than 50% compared to the simple linear regression model and the nonlinear logistic model. The VCM that describes the relationship between water and air temperatures for each stream is represented by slope and intercept curves from the fitted model. In the second part, I consider water and air temperatures for different streams that are spatial correlated. I focus on clustering multiple streams by using intercept and slope curves estimated from the VCM. Spatial information is incorporated to make clustering results geographically meaningful. I further propose a weighted distance as a dissimilarity measure for streams, which provides a flexible framework to interpret the clustering results under different weights. Real data analysis shows that streams in same cluster share similar geographic features such as solar radiation, percent forest and elevation. In the third part, I develop a spatial-temporal VCM (STVCM) to deal with missing data. The STVCM takes both spatial and temporal variation of water temperature into account. I develop a novel estimation method that emphasizes the time effect and treats the space effect as a varying coefficient for the time effect. A simulation study shows that the performance of the STVCM on missing data imputation is better than several existing methods such as the neural network and the Gaussian process. The STVCM is also applied to all 156 streams in this study to obtain a complete data record.
Ph. D.

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Pi, Lira. « Fisher Information in Censored Samples from Univariate and Bivariate Populations and Their Applications ». The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1354851703.

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Zhou, Yahong. « Estimation of transformation models, generalized bivariate probit models, and box-cox partially linear models : three essays in microeconomics / ». View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?ECON%202005%20ZHOU.

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Orjuela, Maria del Pilar. « A Study on the Correlation of Bivariate And Trivariate Normal Models ». FIU Digital Commons, 2013. http://digitalcommons.fiu.edu/etd/976.

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Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.

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Barker, Jolene. « APPLICATIONS OF THE BIVARIATE GAMMA DISTRIBUTION IN NUTRITIONAL EPIDEMIOLOGY AND MEDICAL PHYSICS ». VCU Scholars Compass, 2008. http://scholarscompass.vcu.edu/etd/1623.

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In this thesis the utility of a bivariate gamma distribution is explored. In the field of nutritional epidemiology a nutrition density transformation is used to reduce collinearity. This phenomenon will be shown to result due to the independent variables following a bivariate gamma model. In the field of radiation oncology paired comparison of variances is often performed. The bivariate gamma model is also appropriate for fitting correlated variances. A method for simulating bivariate gamma random variables is presented. This method is used to generate data from several bivariate gamma models and the asymptotic properties of a test statistic, suggested for the radiation oncology application, is studied.

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Li, Mengying. « New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate ». FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1583.

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A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

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Prokosch, Jorinde. « Bivariate Bayesian Model Averaging and Ensemble Model Output Statistics : With a Case Study of Ensemble Temperature Forecasts in Trondheim ». Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-23050.

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In this study a bivariate Bayesian model averaging (BMA) and Ensemble model output statistics (EMOS) technique for ensemble temperature forecasts are proposed to account for lead time dependencies between errors. Also univariate BMA and EMOS techniques are applied to generate calibrated normal predictive density functions. For univariate models, Maximum likelihood estimation (MLE) and minimum Continuous rank probability score (minCRPS) estimation are compared. In addition to the MLE, a sample method to simplify the minimum Energy score (minES) estimation is proposed for bivariate models. In a case study of 2-m surface temperature in Trondheim - Voll between year 2007 and 2011, using the European Center for Medium-Range Weather Forecasts (ECMWF) forecast ensembles, the BMA technique using minCRPS estimation shows the most calibrated and sharpest post-processed probabilistic forecasts. The bivariate EMOS model using minES estimation gives the best score and shows that there is lead time dependencies between errors.

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Knoebel, Bruce R. « An investigation of a bivariate distribution approach to modeling diameter distributions at two points in time ». Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/54310.

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A diameter distribution prediction procedure for single species stands was developed based on the bivariate S_B distribution model. The approach not only accounted for and described the relationships between initial and future diameters and their distributions, but also assumed future diameter given initial diameter to be a random variable. While this method was the most theoretically correct, comparable procedures based on the definition of growth equations which assumed future diameter given initial diameter to be a constant, sometimes provided somewhat better results. Both approaches performed as well, and in some cases, better than the established methods of diameter distribution prediction such as parameter recovery, percentile prediction, and parameter prediction. The approaches based on the growth equations are intuitively and biologically appealing in that the future distribution is determined from an initial distribution and a specified initial-future diameter relationship. ln most appropriate. While this result simplified some procedures, it also implied that the initial and future diameter distributions differed only in location and scale, not in shape. This is a somewhat unrealistic assumption, however, due to the relatively short growth periods and the alterations in stand structure and growth due to the repeated thinnings, the data did not provide evidence against the linear growth equation assumption. The growth equation procedures not only required the initial and future diameter distributions to be of a particular form, but they also restricted the initial-future diameter relationship to be of a particular form. The individual tree model, which required no distributional assumptions or restrictions on the growth equation, proved to be the better approach to use in terms of predicting future stand tables as it performed better than all of the distribution-based approaches. For the bivariate distribution, the direct fit, parameter recovery, parameter prediction and percentile prediction diameter distribution prediction techniques, implied diameter relationships were defined. Evaluations revealed that these equations were both accurate and precise, indicating that the accurate specification of the initial distribution and the diameter diameter distribution.
Ph. D.

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Eren, Emrah. « Effect Of Estimation In Goodness-of-fit Tests ». Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/2/12611046/index.pdf.

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In statistical analysis, distributional assumptions are needed to apply parametric procedures. Assumptions about underlying distribution should be true for accurate statistical inferences. Goodness-of-fit tests are used for checking the validity of the distributional assumptions. To apply some of the goodness-of-fit tests, the unknown population parameters are estimated. The null distributions of test statistics become complicated or depend on the unknown parameters if population parameters are replaced by their estimators. This will restrict the use of the test. Goodness-of-fit statistics which are invariant to parameters can be used if the distribution under null hypothesis is a location-scale distribution. For location and scale invariant goodness-of-fit tests, there is no need to estimate the unknown population parameters. However, approximations are used in some of those tests. Different types of estimation and approximation techniques are used in this study to compute goodness-of-fit statistics for complete and censored samples from univariate distributions as well as complete samples from bivariate normal distribution. Simulated power properties of the goodness-of-fit tests against a broad range of skew and symmetric alternative distributions are examined to identify the estimation effects in goodness-of-fit tests. The main aim of this thesis is to modify goodness-of-fit tests by using different estimators or approximation techniques, and finally see the effect of estimation on the power of these tests.

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Rettiganti, Mallikarjuna Rao. « Statistical Models for Count Data from Multiple Sclerosis Clinical Trials and their Applications ». The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291180207.

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Yu, Li. « Tau-Path Test - A Nonparametric Test For Testing Unspecified Subpopulation Monotone Association ». The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1255657068.

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Li, Wei. « Numerical Modelling and Statistical Analysis of Ocean Wave Energy Converters and Wave Climates ». Doctoral thesis, Uppsala universitet, Elektricitetslära, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-305870.

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Ocean wave energy is considered to be one of the important potential renewable energy resources for sustainable development. Various wave energy converter technologies have been proposed to harvest the energy from ocean waves. This thesis is based on the linear generator wave energy converter developed at Uppsala University. The research in this thesis focuses on the foundation optimization and the power absorption optimization of the wave energy converters and on the wave climate modelling at the Lysekil wave converter test site. The foundation optimization study of the gravity-based foundation of the linear wave energy converter is based on statistical analysis of wave climate data measured at the Lysekil test site. The 25 years return extreme significant wave height and its associated mean zero-crossing period are chosen as the maximum wave for the maximum heave and surge forces evaluation. The power absorption optimization study on the linear generator wave energy converter is based on the wave climate at the Lysekil test site. A frequency-domain simplified numerical model is used with the power take-off damping coefficient chosen as the control parameter for optimizing the power absorption. The results show a large improvement with an optimized power take-off damping coefficient adjusted to the characteristics of the wave climate at the test site. The wave climate modelling studies are based on the wave climate data measured at the Lysekil test site. A new mixed distribution method is proposed for modelling the significant wave height. This method gives impressive goodness of fit with the measured wave data. A copula method is applied to the bivariate joint distribution of the significant wave height and the wave period. The results show an excellent goodness of fit for the Gumbel model. The general applicability of the proposed mixed-distribution method and the copula method are illustrated with wave climate data from four other sites. The results confirm the good performance of the mixed-distribution and the Gumbel copula model for the modelling of significant wave height and bivariate wave climate.

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Belu, Alexandru C. « Multivariate Measures of Dependence for Random Variables and Levy Processes ». Case Western Reserve University School of Graduate Studies / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=case1333396376.

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Lu, Shihai. « Novel Step-Down Multiple Testing Procedures Under Dependence ». Bowling Green State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1416594298.

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Di, Credico Gioia. « Some developments in semiparametric and cross-classified multilevel models ». Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3424946.

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Our work has developed from a real epidemiological problem. The carcinogenic effect of cigarette smoking on head and neck cancer has been extensively studied in the literature highlighting a non linear dose-response relationship. Recently, the use of linear regression splines, within semiparametric models framework, has allowed an improvement in the evaluation of the association between smoking habits and head and neck cancer. Our work focuses on the development of a methodology able to improve several aspects of the estimation of the aforementioned relationship. In particular, the approximation of the spline function, represented by truncated linear basis, has been refined by addressing the problem of estimating two key quantities for the definition of a spline function: the number and position of the knots. The proposed methodology uses a Bayesian approach. We then focused on developing a streamlined methodology applicable to generalised linear models for cross-classified data. In particular, the steps necessary to calculate the covariance matrix are optimised with respect to one of the two random effects, allowing a computational gain both in terms of time and memory usage. The proposed algorithms are applied in the context of the inferential variational methods in detail to the mean field variational Bayes.
Il nostro lavoro si è sviluppato a partire da un problema epidemiologico reale. L’effetto carcinogenico del fumo di sigaretta sui tumori testa-collo è stato ampiamente studiato in letteratura evidenziando una relazione dose-risposta non lineare. Recentemente, l’utilizzo di spline lineari di regressione nell’ambito di modelli semiparametrici, ha permesso un miglioramento nella valutazione dell’associazione tra fumo e tumori testa-collo. Il nostro lavoro si concentra sullo sviluppo di una metodologia capace di migliorare la stima della suddetta relazione sotto diversi aspetti. In particolare, l'approssimazione della funzione spline, rappresentata attraverso basi lineari troncate, è stata affinata affrontando il problema di stima di due quantità chiave per sua la definizione: il numero e la posizione dei nodi. La metodologia proposta si serve di un approccio Bayesiano. Successivamente ci siamo concentrati sullo sviluppo di una metodologia streamline applicabile a modelli lineari generalizzati per dati con struttura cross-classified. In particolare, gli step necessari al calcolo della matrice di covarianza vengono ottimizzati rispetto ad uno dei due effetti random permettendo un guadagno computazionale sia in termini di tempo che di utilizzo della memoria. Gli algoritmi proposti vengono applicati nell’ambito dei metodi variazionali inferenziali nel dettaglio al mean field variational Bayes.

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Saint, Pierre Aude. « Méthodes d'analyse génétique de traits quantitatifs corrélés : application à l'étude de la densité minérale osseuse ». Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00633981.

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La plupart des maladies humaines ont une étiologie complexe avec des facteurs génétiques et environnementaux qui interagissent. Utiliser des phénotypes corrélés peut augmenter la puissance de détection de locus de trait quantitatif. Ce travail propose d'évaluer différentes approches d'analyse bivariée pour des traits corrélés en utilisant l'information apportée par les marqueurs au niveau de la liaison et de l'association. Le gain relatif de ces approches est comparé aux analyses univariées. Ce travail a été appliqué à la variation de la densité osseuse à deux sites squelettiques dans une cohorte d'hommes sélectionnés pour des valeurs phénotypiques extrêmes. Nos résultats montrent l'intérêt d'utiliser des approches bivariées en particulier pour l'analyse d'association. Par ailleurs, dans le cadre du groupe de travail GAW16, nous avons comparé les performances relatives de trois méthodes d'association dans des données familiales.

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Tognaccini, Sofia. « Geomorfologia applicata all'individuazione dello stato di attività dei movimenti gravitativi e analisi di suscettibilità da frana in diversi contesti geologico-strutturali ». Doctoral thesis, 2019. http://hdl.handle.net/2158/1198143.

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Le analisi contenute nel presente elaborato di tesi costituiscono uno strumento conoscitivo di base, indispensabile per tutte quelle zone in cui i movimenti franosi o altre dinamiche inducono pericolosità geologica interferendo con l’ambiente e le strutture antropiche, consentendo una buona conoscenza, anche di territori con estensione piuttosto ampia, a costi molto ridotti.Tutte le procedure e software utilizzati nel presente lavoro sono disponibili open-source e fruibili gratuitamente online. Il rilevamento geomorfologico è stato condotto in tre aree di studio, caratterizzate da contesti geologico-strutturali diversi tra loro. Tale rilevamento, coadiuvato da un'analisi multitemporale condotta mediante fotointerpretazione, si è rivelato molto utile per individuare i limiti dei movimenti franosi, il loro grado di attività e la loro evoluzione nel tempo. Le analisi statistiche hanno consentito di individuare la variabilità dei parametri predisponenti nelle diverse aree di studio e di indicare quali classi, tra i parametri, sono caratterizzate dal maggior numero di frane e, dunque, più prone al franamento. Gli studi di suscettibilità effettuati per le diverse aree di studio con la metodologia di statistica bivariata mostrano un’elevata percentuale di aree in frana ricadenti all’interno delle aree predette a più elevata suscettibilità e possono essere applicati sia a piccola sia a grande scala, per diverse tipologie di frane. Infine, i risultati ottenuti tramite il modello prevalentemente deterministico basato sul modulo r.slope.stability (http://www.slopestability.org/) sono piuttosto attendibili e rappresentativi della situazione reale, come dimostrato dai risultati della validazione tramite la stima di AROC. L’opportunità di utilizzare software GIS, non solo per la manipolazione dei dati ma anche per il loro aggiornamento e per l’esecuzione automatica delle procedure bivariate (ad es. attraverso il codice in linguaggio Python creato durante questo lavoro di tesi), incrementa notevolmente la possibilità di estendere queste analisi a nuove e diverse aree di studio, con costi pressoché nulli.

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HUSEMANN, JOYCE ANN STEVENS. « HISTOGRAM ESTIMATORS OF BIVARIATE DENSITIES (MULTIVARIATE, STATISTICS) ». Thesis, 1986. http://hdl.handle.net/1911/15984.

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One-dimensional fixed-interval histogram estimators of univariate probability density functions are less efficient than the analogous variable-interval estimators which are constructed from intervals whose lengths are determined by the criterion of integrated mean squared error (IMSE) minimization. Similarly, two-dimensional fixed-cell-size histogram estimators of bivariate probability density functions are less efficient than variable-cell-size estimators whose cell sizes are determined from IMSE minimization. Only estimators whose cell sides are parallel to the coordinate axes are examined. The estimators are classified according to the functional dependence of their cell dimensions upon x and y: each cell dimension of the Minimally Restricted Mesh depends upon both x and y; one cell dimension of the Semi-fixed-dimension Mesh is fixed, and the other depends upon either x alone or y alone; one cell dimensions of the Variable-dimensions Mesh I depends upon x and the other upon y; one cell dimension of the Variable-dimension Mesh II depends upon x alone or y alone and the other depends upon both x and y. The Minimally Restricted Mesh results in the smallest IMSE of the four types, but is not implementable. The other meshes are implementable and are listed above in order of decreasing IMSE. Random vectors from Dirichlet, mixed bivariate and elliptical bivariate normal distributions were generated and used to construct optimal histograms. The Variable-dimension Mesh II produced histograms having IMSEs from 20 to 90 percent smaller than those from histograms based upon optimal fixed-dimension meshes. The most substantial improvements were observed for mixed bivariate normal densities having strongly unequal variances. Modest improvements (20%) were observed for skewed densities and slightly elliptical densities, but no improvements were observed in cases of highly elliptical densities whose axes were rotated 45(DEGREES) from the coordinate axes.

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Hua, Wen-Yu, et 花文妤. « Statistical Inference for Bivariate Survival Data Based on ». Thesis, 2007. http://ndltd.ncl.edu.tw/handle/85460855612746920449.

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碩士
國立交通大學
統計學研究所
95
The thesis considers semi-parametric inference based on Copula models for bivariate survival data subject to right censoring. There exist several semi-parametric inference approaches to estimating the association parameter. We examine and compare three approaches developed for homogeneous data in absence of covariates. Then we extend these methods to a regression setting that accounts for marginal heterogeneity explained by the covariates. Finite-sample performances are examined by simulations.

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Ghebremichael, Musie S. « Nonparametric estimation of bivariate mean residual life function ». Thesis, 2005. http://hdl.handle.net/1911/18764.

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In survival analysis the additional lifetime that an object survives past a time t is called the residual life function of the object. Mathematically speaking if the lifetime of the object is described by a random variable T then the random variable R(t) = [T - t| T > t] is called the residual life random variable. The quantity e(t) = E( R(t)) = E[T - t|T > t] is called the mean residual lifetime (mrl) function or the life expectancy at age t. There are numerous situations where the bivariate mrl function is important. Times to death or times to initial contraction of a disease may be of interest for litter mate pairs of rats or for twin studies in humans. The time to a deterioration level or the time to reaction of a treatment may be of interest in pairs of lungs, kidneys, breasts, eyes or ears of humans. In reliability, the distribution of the lifelengths of a particular pair of components in a system may be of interest. Because of the dependence among the event times, we can not get reliable results by using the univariate mrl function on each event times in order to study the aging process. The bivariate mrl function is useful in analyzing the joint distribution of two event times where these times are dependent. In recent years, though considerable attention has been paid to the univariate mrl function, relatively little research has been devoted to the analysis of the bivariate mrl function. The specific contribution of this dissertation consists in proposing, and examining the properties of, nonparametric estimators of the bivariate mean residual life function when a certain order among such functions exists. That is, we consider the problem of nonparametric estimation of a bivariate mrl function when it is bounded from above by another known or unknown mrl function. The estimators under such an order constraint are shown to perform better than the empirical mrl function in terms of mean squared error. Moreover, they are shown to be projections, onto an appropriate space, of the empirical mean residual life function. Under suitable technical conditions, the asymptotic theory of these estimators is derived. Finally, the procedures are applied to a data set on bivariate survival. More specifically, we have used the Diabetic Retinopathy Study (DRS) data to illustrate our estimators. In this data set, the survival times of both left and right eyes are given for two groups of patients: juvenile and adult diabetics. Thus, it seems natural to assume that the mrl for the juvenile diabetics be longer than the mrl of the adult diabetics. Under this assumption, we calculated the estimators of the mrl function for each group. We have also calculated the empirical mrl functions of the two groups and compared them with the estimators of the mrl function obtained under the above assumption.

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Chandra, Krishnendu. « Survival Analysis using Bivariate Archimedean Copulas ». Thesis, 2015. https://doi.org/10.7916/D80Z72F0.

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In this dissertation we solve the nonidentifiability problem of Archimedean copula models based on dependent censored data (see [Wang, 2012]). We give a set of identifiability conditions for a special class of bivariate frailty models. Our simulation results show that our proposed model is identifiable under our proposed conditions. We use EM algorithm to estimate unknown parameters and the proposed estimation approach can be applied to fit dependent censored data when the dependence is of research interest. The marginal survival functions can be estimated using the copula-graphic estimator (see [Zheng and Klein, 1995] and [Rivest and Wells, 2001]) or the estimator proposed by [Wang, 2014]. We also propose two model selection procedures for Archimedean copula models, one for uncensored data and the other one for right censored bivariate data. Our simulation results are similar to that of [Wang and Wells, 2000] and suggest that both procedures work quite well. The idea of our proposed model selection procedure originates from the model selection procedure for Archimedean copula models proposed by [Wang and Wells, 2000] for right censored bivariate data using the L2 norm corresponding to the Kendall distribution function. A suitable bootstrap procedure is yet to be suggested for our method. We further propose a new parameter estimator and a simple goodness-of-fit test for Archimedean copula models when the bivariate data is under fixed left truncation. Our simulation results suggest that our procedure needs to be improved so that it can be more powerful, reliable and efficient. In our strategy, to obtain estimates for the unknown parameters, we heavily exploit the concept of truncated tau (a measure of association established by [Manatunga and Oakes, 1996] for left truncated data). The idea of our goodness of fit test originates from the goodness-of-fit test for Archimedean copula models proposed by [Wang, 2010] for right censored bivariate data.

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Chiu, Chuan-Hung, et 邱全宏. « A Family of Bivariate Distributions With Some Applications to Statistical Inferences ». Thesis, 2005. http://ndltd.ncl.edu.tw/handle/10145438551162546696.

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碩士
淡江大學
管理科學研究所碩士班
93
In chapter 1, we have proposed a new family of bivariate distributions, and also some special distributions such as bivariate exponential, bivariate Weibull etc.. Some comparisons with known results are also made. A real data set is illustrated in which some parameters are estimated by moment method. In chapter 2, we consider an error-in-variables regression model for random fatigue-limit problem. Some estimates for the related parameters are also derived. A real data set is also illustrated by the proposed method and some comparisons are also made with known results. Some simulation study is also carried out.

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Greenberg, Simon L. « Bivariate goodness-of-fit tests based on Kolmogorov-Smirnov type statistics ». Thesis, 2008. http://hdl.handle.net/10210/437.

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Hsu, Hsiang-Ling, et 許湘伶. « Optimal designs for statistical inferences in nonlinear models with bivariate response variables ». Thesis, 2011. http://ndltd.ncl.edu.tw/handle/10736549502397202508.

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博士
國立中山大學
應用數學系研究所
99
Bivariate or multivariate correlated data may be collected on a sample of unit in many applications. When the experimenters concern about the failure times of two related subjects for example paired organs or two chronic diseases, the bivariate binary data is often acquired. This type of data consists of a observation point x and indicators which represent whether the failure times happened before or after the observation point. In this work, the observed bivariate data can be written with the following form {x, δ1=I(X1≤ x), δ2=I(X2≤ x)}.The corresponding optimal design problems for parameter estimation under this type of bivariate data are discussed. For this kind of the multivariate responses with explanatory variables, their marginal distributions may be from different distributions. Copula model is a way to formulate the relationship of these responses, and the association between pairs of responses. Copula models for bivariate binary data are considered useful in practice due to its flexibility. In this dissertation for bivariate binary data, the marginal functions are assumed from exponential or Weibull distributions and two assumptions, independent or correlated, about the joint function between variables are considered. When the bivariate binary data is assumed correlated, the Clayton copula model is used as the joint cumulative distribution function. There are few works addressed the optimal design problems for bivariate binary data with copula models. The D-optimal designs aim at minimizing the volume of the confidence ellipsoid for estimating unknown parameters including the association parameter in bivariate copula models. They are used to determine the best observation points. Moreover, the Ds-optimal designs are mainly used for estimation of the important association parameter in Clayton model. The D- and Ds-optimal designs for the above copula model are found through the general equivalence theorem with numerical algorithm. Under different model assumptions, it is observed that the number of support points for D-optimal designs is at most as the number of model parameters for the numerical results. When the difference between the marginal distributions and the association are significant, the association becomes an influential factor which makes the number of supports gets larger. The performances of estimation based on optimal designs are reasonably well by simulation studies. In survival experiments, the experimenter customarily takes trials at some specific points such as the position of the 25, 50 and 75 percentile of distributions. Hence, we consider the design efficiencies when the design points for trials are at three or four particular percentiles. Although it is common in practice to take trials at several quantile positions, the allocations of the proportion of sample size also have great influence on the experimental results. To use a locally optimal design in practice, the prior information for models or parameters are needed. In case there is not enough prior knowledge about the models or parameters, it would be more flexible to use sequential experiments to obtain information in several stages. Hence with robustness consideration, a sequential procedure is proposed by combining D- and Ds-optimal designs under independent or correlated distribution in different stages of the experiment. The simulation results based on the sequential procedure are compared with those by the one step procedures. When the optimal designs obtained from an incorrect prior parameter values or distributions, those results may have poor efficiencies. The sample mean of estimators and corresponding optimal designs obtained from sequential procedure are close to the true values and the corresponding efficiencies are close to 1. Huster (1989) analyzed the corresponding modeling problems for the paired survival data and applied to the Diabetic Retinopathy Study. Huster (1989) considered the exponential and Weibull distributions as possible marginal distributions and the Clayton model as the joint function for the Diabetic Retinopathy data. This data was conducted by the National Eye Institute to assess the effectiveness of laser photocoagulation in delaying the onset of blindness in patients with diabetic retinopathy. This study can be viewed as a prior experiment and provide the experimenter some useful guidelines for collecting data in future studies. As an application with Diabetic Retinopathy Study, we develop optimal designs to collect suitable data and information for estimating the unknown model parameters. In the second part of this work, the optimal design problems for parameter estimations are considered for the type of proportional data. The nonlinear model, based on Jorgensen (1997) and named the dispersion model, provides a flexible class of non-normal distributions and is considered in this research. It can be applied in binary or count responses, as well as proportional outcomes. For continuous proportional data where responses are confined within the interval (0,1), the simplex dispersion model is considered here. D-optimal designs obtained through the corresponding equivalence theorem and the numerical results are presented. In the development of classical optimal design theory, weighted polynomial regression models with variance functions which depend on the explanatory variable have played an important role. The problem of constructing locally D-optimal designs for simplex dispersion model can be viewed as a weighted polynomial regression model with specific variance function. Due to the complex form of the weight function in the information matrix is considered as a rational function, an approximation of the weight function and the corresponding optimal designs are obtained with different parameters. These optimal designs are compared with those using the original weight function.

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« Multiple comparison procedures for a latent variable model with bivariate ordered categorical responses ». 2012. http://library.cuhk.edu.hk/record=b5549561.

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在許多實驗研究中，實驗數據經常由有序觀測數據組成，這樣的例子很容易在醫學、臨床研究、社會學或心理學的研究中找到。一般有兩種方法可以用來分析有序分類數據。第一種方法是基於Wilcoxon-Mann-Whitney 統計量的非參數方法，第二種方法是把響應變量看成是某個連續潛變量模型的一種表現的潛變量模型。在本論文中，我們主要研究基於潛變量模型對具有一維或二維有序分類響應變量的處理的比較問題，同時解決具有一維有序分類數據的多重比較過程的功效及樣本量的確定問題。
潛變量模型已經被應用于對具有一維有序分類觀測數據的含有對照組的多重比較中。這種方法可以很好地應用于臨床研究中對含有對照組的不同治療方法的效用比較問題。在本論文的第一部份中，我們致力於把這種思想推廣到成對多重比較，成對多重比較是臨床研究中另一個很重要的課題。我們通過隨機模擬來對不同的方法在控制整體第一類錯誤和功效的優勢進行評估。在本論文的第二部份，我們主要研究具有二維有序分類響應變量的多重比較過程。在這些過程中，我們把二維有序分類數據看成是某個潛二維變量的一種表現。非參數方法也經常被應用於做兩個處理的比較問題。然而在本文中，我們對非參數方法的劣勢進行了說明。處理具有二維有序分類響應變量的含有對照組的多重比較問題是本論文的研究重點。基於潛變量模型的方法，我們給出了含有對照組的多重比較的若干檢驗過程，包括單步檢驗過程和逐步檢驗過程。在論文的第三部份，我們對具有一維有序分類數據的含有對照組的多重比較過程的功效和樣本量的確定問題進行了討論。基於Lu, Poon and Cheung (2012) 建議的多重比較過程，我們得到了滿足一定功效的樣本量的確定方法，并通過實例進行了說明。
In many scientific studies, research data are frequently composed of ordered categorical observations. Numerous examples could easily be found in areas including medical and clinical studies, sociology and psychology. There are two popular approaches in analyzing ordered categorical data. One is to employ the non-parametric method based on the Wilcoxon-Mann-Whitney statistics. The other is to use the latent variable model that conceptualizes the responses as manifestations of some underlying continuous variables. In this project, we focus on the comparisons of different populations with either univariate or bivariate ordered categorical observations using a latent variable model. The study of power and sample size requirement for multiple testing with univariate ordered categorical data are also provided in this thesis.
For univariate ordered categorical observations, the latent variable model has been used to compare treatments with a control. The developed methods are useful for applications in clinical studies where one would like to compare the efficacy of different treatments with a given control/placebo. In this thesis, we seek to extend this idea to develop the useful procedures for pairwise multiple comparisons which are often important objectives of clinical trials. Extensive simulation studies regarding overall type I error rate and power are performed to evaluate the merits of different procedures.
The second part of this thesis is devoted to multiple comparison methods with bivariate ordered categorical responses under the assumption that the bivariate ordered categorical data are manifestations of an underlying bivariate normal distribution. To compare two population mean vectors, nonparametric procedures are also frequently being used, but as demonstrated in this thesis, these methods are inferior to testing procedures based on the latent variable model. Hence, by the adoption of the latent variable model, we develop procedures that can be used to conduct multiple comparisons with a control for bivariate categorical responses. Different multiple comparison mechanisms including single-step and stepwise procedures are explored. Numerical examples for illustrative purposes are also given.
For the last part of this thesis, we discuss power and sample size determination for multiple comparisons with control for univariate ordered categorical data. Based on the multiple testing procedures proposed by Lu, Poon and Cheung (2012), we derive the procedure to compute the required sample size that guarantee a pre-specified power level. Numerical examples are also given.
For the last part of this thesis, we discuss power and sample size determination for multiple comparisons with control for univariate ordered categorical data. Based on the multiple testing procedures proposed by Lu, Poon and Cheung (2012), we derive the procedure to compute the required sample size that guarantee a pre-specified power level. Numerical examples are also given.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Lin, Yueqiong.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2012.
Includes bibliographical references (leaves 92-100).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.
Abstract --- p.i
Acknowledgement --- p.iv
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Overview --- p.1
Chapter 1.2 --- Outline of the thesis --- p.4
Chapter 2 --- Pairwise Comparisons with Ordered Categorical Responses --- p.6
Chapter 2.1 --- Introduction --- p.6
Chapter 2.2 --- Proportional odds model --- p.8
Chapter 2.3 --- Latent variable model --- p.11
Chapter 2.4 --- Pairwise comparisons --- p.15
Chapter 2.4.1 --- Single-step procedure and the computation of critical values . --- p.15
Chapter 2.4.2 --- Approximation of critical values --- p.16
Chapter 2.4.3 --- A single-step conservative testing procedure: the Bonferroni procedure --- p.18
Chapter 2.4.4 --- A step-wise testing procedure: Hochberg's step-up procedure . --- p.19
Chapter 2.5 --- Simulation: power comparison --- p.20
Chapter 2.6 --- Examples --- p.24
Chapter 2.7 --- Conclusion --- p.28
Chapter 3 --- Multiple comparison procedures for a latent variable model with bivariate ordered categorical responses --- p.29
Chapter 3.1 --- Introduction --- p.29
Chapter 3.2 --- Latent bivariate normal model --- p.31
Chapter 3.2.1 --- The model --- p.31
Chapter 3.2.2 --- Model specification --- p.33
Chapter 3.2.3 --- Test Statistics --- p.35
Chapter 3.2.4 --- Statistical inference --- p.35
Chapter 3.3 --- Nonparametric test --- p.37
Chapter 3.3.1 --- Test statistic --- p.39
Chapter 3.3.2 --- A Comparison between the latent variable model procedure and nonparametric tests --- p.42
Chapter 3.4 --- Multiple comparisons of several treatments with a control based on the latent variable model --- p.47
Chapter 3.5 --- Simulation --- p.51
Chapter 3.6 --- Examples --- p.56
Chapter 3.7 --- Conclusion --- p.59
Chapter 4 --- Sample size determination for multiple comparisons with ordered univariate categorical data --- p.62
Chapter 4.1 --- Introduction --- p.62
Chapter 4.2 --- Multiple comparisons of treatments a control with ordered categorical responses --- p.64
Chapter 4.3 --- Power function --- p.67
Chapter 4.4 --- Sample size determination and tables --- p.75
Chapter 4.5 --- Examples --- p.85
Chapter 4.6 --- Conclusion --- p.88
Chapter 5 --- Further Research --- p.90
Bibliography --- p.92
Appendix
Chapter A --- Procedures to obtain the MLE of parameter θ₀ --- p.101
Chapter B --- Nonparametric test --- p.105
Chapter C --- Procedures to obtain the critical value for Dunnett's single-step procedure --- p.109
Chapter D --- Procedures to obtain the critical value for Dunnett's single-step procedure with balanced homogeneous groups --- p.112

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Okyere, Ebenezer. « Maximum Likelihood Analysis for Bivariate Exponential Distributions ». Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B395-F.

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