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1
Liero, Hannelore. "Goodness of Fit Tests of L2-Type". Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2011/5149/.
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We give a survey on procedures for testing functions which are based on quadratic deviation measures. The following problems are considered: Testing whether a density function lies in a parametric class of functions, whether continuous random variables are independent; testing cell probabilities and independence in sparse data sets; testing the parametric fit of a regression homoscedasticity in a regression model and testing the hazard rate in survival models with censoring and with and without covariates.
2
Hallett, David C. "Goodness of fit tests in logistic regression". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq45403.pdf.
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Zhang, Jin. "Powerful goodness-of-fit and multisample tests". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ66371.pdf.
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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.
5
Liu, Tianyi. "Power Comparison of Some Goodness-of-fit Tests". FIU Digital Commons, 2016. http://digitalcommons.fiu.edu/etd/2572.
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There are some existing commonly used goodness-of-fit tests, such as the Kolmogorov-Smirnov test, the Cramer-Von Mises test, and the Anderson-Darling test. In addition, a new goodness-of-fit test named G test was proposed by Chen and Ye (2009). The purpose of this thesis is to compare the performance of some goodness-of-fit tests by comparing their power.
A goodness-of-fit test is usually used when judging whether or not the underlying population distribution differs from a specific distribution. This research focus on testing whether the underlying population distribution is an exponential distribution.
To conduct statistical simulation, SAS/IML is used in this research. Some alternative distributions such as the triangle distribution, V-shaped triangle distribution are used. By applying Monte Carlo simulation, it can be concluded that the performance of the Kolmogorov-Smirnov test is better than the G test in many cases, while the G test performs well in some cases.
6
Cigsar, Candemir. "Goodness-of-fit Tests Based On Censored Samples". Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/2/12606226/index.pdf.
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In this study, the most prominent goodness-of-fit tests for censored samples are reviewed. Power properties of goodness-of-fit statistics of the null hypothesis that a sample which is censored from right, left and both right and left which comes from uniform, normal and exponential distributions are investigated. Then, by a similar argument extreme value, student t with 6 degrees of freedom and generalized logistic distributions are discussed in detail through a comprehensive simulation study. A variety of real life applications are given. Suitable test statistics for testing the above distributions for censored samples are also suggested in the conclusion.
7
Lü, Wei, i 吕薇. "On some goodness-of-fit tests for copulas". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B47849964.
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Copulas have been known in the statistical literature for many years, and
have become useful tools in modeling dependence structure of multivariate
random variables, overcoming some of the drawbacks of the commonly-used
correlation measures. Goodness-of-fit tests for copulas play a very important
role in evaluating the suitability of a potential input copula model. In recent
years, many approaches have been proposed for constructing goodness-of-fit
tests for copula families. Among them, the so-called “blanket tests" do not
require an arbitrary data categorization or any strategic choice of weight function, smoothing parameter, kernel, and so on.
As preliminaries, some background and related results of copulas are firstly
presented. Three goodness-of-fit test statistics belonging to the blanket test
classification are then introduced. Since the asymptotic distributions of the
test statistics are very complicated, parametric bootstrap procedures are employed to approximate critical values of the test statistics under the null hypotheses. To assess the performance of the three test statistics in the low
dependence cases, simulation studies are carried out for three bivariate copula families, namely the Gumbel-Hougaard copula family, the Ali-Mikhail-Haq
copula family, and the Farlie-Gumbel-Morgenstern copula family. Specifically
the effect of low dependence on the empirical sizes and powers of the three
blanket tests under various combinations of null and alternative copula families are examined. Furthermore, to check the performance of the three tests
for higher dimensional copulas, the simulation studies are extended to some
three-dimensional copulas. Finally the three goodness-of-fit tests are applied
to two real data sets.published_or_final_version
Statistics and Actuarial Science
Master
Master of Philosophy
8
Kpanzou, Tchilabalo Abozou. "Aspects of copulas and goodness-of-fit". Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019/1949.
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Steele, Michael C., i n/a. "The Power of Categorical Goodness-Of-Fit Statistics". Griffith University. Australian School of Environmental Studies, 2003. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20031006.143823.
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The relative power of goodness-of-fit test statistics has long been debated in the literature. Chi-Square type test statistics to determine 'fit' for categorical data are still dominant in the goodness-of-fit arena. Empirical Distribution Function type goodness-of-fit test statistics are known to be relatively more powerful than Chi-Square type test statistics for restricted types of null and alternative distributions. In many practical applications researchers who use a standard Chi-Square type goodness-of-fit test statistic ignore the rank of ordinal classes. This thesis reviews literature in the goodness-of-fit field, with major emphasis on categorical goodness-of-fit tests. The continued use of an asymptotic distribution to approximate the exact distribution of categorical goodness-of-fit test statistics is discouraged. It is unlikely that an asymptotic distribution will produce a more accurate estimation of the exact distribution of a goodness-of-fit test statistic than a Monte Carlo approximation with a large number of simulations. Due to their relatively higher powers for restricted types of null and alternative distributions, several authors recommend the use of Empirical Distribution Function test statistics over nominal goodness-of-fit test statistics such as Pearson's Chi-Square. In-depth power studies confirm the views of other authors that categorical Empirical Distribution Function type test statistics do not have higher power for some common null and alternative distributions. Because of this, it is not sensible to make a conclusive recommendation to always use an Empirical Distribution Function type test statistic instead of a nominal goodness-of-fit test statistic. Traditionally the recommendation to determine 'fit' for multivariate categorical data is to treat categories as nominal, an approach which precludes any gain in power which may accrue from a ranking, should one or more variables be ordinal. The presence of multiple criteria through multivariate data may result in partially ordered categories, some of which have equal ranking. This thesis proposes a modification to the currently available Kolmogorov-Smirnov test statistics for ordinal and nominal categorical data to account for situations of partially ordered categories. The new test statistic, called the Combined Kolmogorov-Smirnov, is relatively more powerful than Pearson's Chi-Square and the nominal Kolmogorov-Smirnov test statistic for some null and alternative distributions. A recommendation is made to use the new test statistic with higher power in situations where some benefit can be achieved by incorporating an Empirical Distribution Function approach, but the data lack a complete natural ordering of categories. The new and established categorical goodness-of-fit test statistics are demonstrated in the analysis of categorical data with brief applications as diverse as familiarity of defence programs, the number of recruits produced by the Merlin bird, a demographic problem, and DNA profiling of genotypes. The results from these applications confirm the recommendations associated with specific goodness-of-fit test statistics throughout this thesis.
10
Steele, Michael C. "The Power of Categorical Goodness-Of-Fit Statistics". Thesis, Griffith University, 2003. http://hdl.handle.net/10072/366717.
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The relative power of goodness-of-fit test statistics has long been debated in the literature. Chi-Square type test statistics to determine 'fit' for categorical data are still dominant in the goodness-of-fit arena. Empirical Distribution Function type goodness-of-fit test statistics are known to be relatively more powerful than Chi-Square type test statistics for restricted types of null and alternative distributions. In many practical applications researchers who use a standard Chi-Square type goodness-of-fit test statistic ignore the rank of ordinal classes. This thesis reviews literature in the goodness-of-fit field, with major emphasis on categorical goodness-of-fit tests. The continued use of an asymptotic distribution to approximate the exact distribution of categorical goodness-of-fit test statistics is discouraged. It is unlikely that an asymptotic distribution will produce a more accurate estimation of the exact distribution of a goodness-of-fit test statistic than a Monte Carlo approximation with a large number of simulations. Due to their relatively higher powers for restricted types of null and alternative distributions, several authors recommend the use of Empirical Distribution Function test statistics over nominal goodness-of-fit test statistics such as Pearson's Chi-Square. In-depth power studies confirm the views of other authors that categorical Empirical Distribution Function type test statistics do not have higher power for some common null and alternative distributions. Because of this, it is not sensible to make a conclusive recommendation to always use an Empirical Distribution Function type test statistic instead of a nominal goodness-of-fit test statistic. Traditionally the recommendation to determine 'fit' for multivariate categorical data is to treat categories as nominal, an approach which precludes any gain in power which may accrue from a ranking, should one or more variables be ordinal. The presence of multiple criteria through multivariate data may result in partially ordered categories, some of which have equal ranking. This thesis proposes a modification to the currently available Kolmogorov-Smirnov test statistics for ordinal and nominal categorical data to account for situations of partially ordered categories. The new test statistic, called the Combined Kolmogorov-Smirnov, is relatively more powerful than Pearson's Chi-Square and the nominal Kolmogorov-Smirnov test statistic for some null and alternative distributions. A recommendation is made to use the new test statistic with higher power in situations where some benefit can be achieved by incorporating an Empirical Distribution Function approach, but the data lack a complete natural ordering of categories. The new and established categorical goodness-of-fit test statistics are demonstrated in the analysis of categorical data with brief applications as diverse as familiarity of defence programs, the number of recruits produced by the Merlin bird, a demographic problem, and DNA profiling of genotypes. The results from these applications confirm the recommendations associated with specific goodness-of-fit test statistics throughout this thesis.Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
Australian School of Environmental Studies
Full Text
11
Jager, Leah R. "Goodness-of-fit statistics based on phi-divergences /". Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/8965.
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Feng, Huijun. "Goodness-of-fit test and bilinear model". Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/47722.
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The Empirical Likelihood method (ELM) was introduced by A. B. Owen to test hypotheses in the early 1990s. It's a nonparametric method and uses the data directly to do statistical tests and to compute confidence intervals/regions. Because of its distribution free property and generality, it has been studied extensively and employed widely in statistical topics. There are many classical test statistics such as the Cramer-von Mises (CM)
test statistic, the Anderson-Darling test statistic, and the Watson test statistic, to name a few. However, none is universally most powerful. This thesis is dedicated to extending the ELM to several interesting statistical topics in hypothesis tests. First of all, we focus on testing the fit of distributions. Based on the CM test, we propose a novel Jackknife Empirical
Likelihood test via estimating equations in testing the goodness-of-fit. The proposed new test
allows one to add more relevant constraints so as to improve the power. Also, this idea can be generalized to other classical test statistics. Second, when aiming at testing the error distributions generated from a statistical model (e.g., the regression model), we introduce the Jackknife Empirical Likelihood idea to the regression model, and further compute the confidence regions with the merits of distribution free limiting chi-square property. Third, the ELM
based on some weighted score equations are proposed for constructing confidence intervals
for the coefficient in the simple bilinear model. The effectiveness of all presented methods are demonstrated by some extensive simulation studies.
13
Li, Yi. "Goodness-of-Fit Tests For Dirichlet Distributions With Applications". Bowling Green State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1435003723.
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Wang, Jingbo. "On the computation and power of goodness-of-fit tests". Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B31998653.
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Wang, Jingbo, i 王靜波. "On the computation and power of goodness-of-fit tests". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B31998653.
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Jia, Weijia. "Goodness-of-fit tests in measurement error models with replications". Diss., Kansas State University, 2018. http://hdl.handle.net/2097/38660.
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Doctor of PhilosophyDepartment of Statistics
Weixing Song
In this dissertation, goodness-of-fit tests are proposed for checking the adequacy of parametric distributional forms of the regression error density functions and the error-prone predictor density function in measurement error models, when replications of the surrogates of the latent variables are available. In the first project, we propose goodness-of-fit tests on the density function of the regression error in the errors-in-variables model. Instead of assuming that the distribution of the measurement error is known as is done in most relevant literature, we assume that replications of the surrogates of the latent variables are available. The test statistic is based upon a weighted integrated squared distance between a nonparametric estimate and a semi-parametric estimate of the density functions of certain residuals. Under the null hypothesis, the test statistic is shown to be asymptotically normal. Consistency and local power results of the proposed test under fixed alternatives and local alternatives are also established. Finite sample performance of the proposed test is evaluated via simulation studies. A real data example is also included to demonstrate the application of the proposed test. In the second project, we propose a class of goodness-of-fit tests for checking the parametric distributional forms of the error-prone random variables in the classic additive measurement error models. We also assume that replications of the surrogates of the error-prone variables are available. The test statistic is based upon a weighted integrated squared distance between a non-parametric estimator and a semi-parametric estimator of the density functions of the averaged surrogate data. Under the null hypothesis, the minimum distance estimator of the distribution parameters and the test statistics are shown to be asymptotically normal. Consistency and local power of the proposed tests under fixed alternatives and local alternatives are also established. Finite sample performance of the proposed tests is evaluated via simulation studies.
17
Gabrys, Robertas. "Goodness-of-Fit and Change-Point Tests for Functional Data". DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/658.
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A test for independence and identical distribution of functional observations is proposed in this thesis. To reduce dimension, curves are projected on the most important functional principal components. Then a test statistic based on lagged cross--covariances of the resulting vectors is constructed. We show that this dimension reduction step introduces asymptotically negligible terms, i.e. the projections behave asymptotically as iid vector--valued observations. A complete asymptotic theory based on correlations of random matrices, functional principal component expansions, and Hilbert space techniques is developed. The test statistic has chi-square asymptotic null distribution.
Two inferential tests for error correlation in the functional linear model are put forward. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distributions are chi--squared with known numbers of degrees of freedom (different for the two forms).
A test for detecting a change point in the mean of functional observations is developed. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution. A comprehensive asymptotic theory for the estimation of a change--point in the mean function of functional observations is developed.
The procedures developed in this thesis can be readily computed using the R package fda. All theoretical insights obtained in this thesis are confirmed by simulations and illustrated by real life-data examples.
18
Chi, Yunchan. "Comparisons of several goodness-of-fit tests for proportional hazards models /". The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487591658175588.
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Mair, Patrick, Ingwer Borg i Thomas Rusch. "Goodness-of-Fit Assessment in Multidimensional Scaling and Unfolding". Taylor & Francis Group, 2016. http://epub.wu.ac.at/5354/1/mairetal2016.pdf.
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Judging goodness of fit in multidimensional scaling requires a comprehensive set of diagnostic tools instead of relying on stress rules of thumb. This article elaborates on corresponding strategies and gives practical guidelines for researchers to obtain a clear picture of the goodness of fit of a solution. Special emphasis will be placed on the use of permutation tests. The second part of the article focuses on goodness-of-fit assessment of an important variant of multidimensional scaling called unfolding, which can be applied to a broad range of psychological data settings. Two real-life data sets are presented in order to walk the reader through the entire set of diagnostic measures, tests, and plots. R code is provided as supplementary information that makes the whole goodness-of-fit assessment workflow, as presented in this article, fully reproducible.
20
Percy, Edward Richard. "Corrected LM goodness-of-fit tests with applicaton to stock returns". Columbus, Ohio : Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1134416514.
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Percy, Edward Richard Jr. "Corrected LM goodness-of-fit tests with applicaton to stock returns". The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1134416514.
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Sharma, Abha. "A distribution-free goodness-of-fit approach to testing in a two-way layout /". The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487323583621853.
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Woo, Pao-sun. "Parametric inference for time series based upon goodness-of-fit /". Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B23472613.
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鄧雅恩 i Nga-yan Fancy Tang. "Resampling tests for some survival models". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31226759.
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Tang, Nga-yan Fancy. "Resampling tests for some survival models /". Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B23457338.
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Chand, Sohail. "Goodness of fit tests and lasso variable selection in time series analysis". Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/12019/.
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This thesis examines various aspects of time series and their applications. In the rst part, we study numerical and asymptotic properties of Box-Pierce family of portmanteau tests. We compare size and power properties of time series model diagnostic tests using their asymptotic c2 distribution and bootstrap distribution (dynamic and fixed design) against various linear and non-linear alternatives. In general, our results show that dynamic bootstrapping provides a better approximation of the distribution underlying these statistics. Moreover, we find that Box-Pierce type tests are powerful against linear alternatives while the CvM due to Escanciano (2006b) test performs better against non linear alternative models. The most challenging scenario for these portmanteau tests is when the process is close to the stationary boundary and value of m, the maximum lag considered in the portmanteau test, is very small. In these situations, the c2 distribution is a poor approximation of the null asymptotic distribution. Katayama (2008) suggested a bias correction term to improve the approximation in these situations. We numerically study Katayama's bias correction in Ljung and Box (1978) test. Our results show that Katayama's correction works well and conrms the results as shown in Katayama (2008). We also provide a number of algorithms for performing the necessary calculations efciently. We notice that the bootstrap automatically does bias correction in Ljung-Box statistic. It motivates us to look at theoretical properties of the dynamic bootstrap in this context. Moreover, noticing the good performance of Katayama's correction, we suggest a bias correction term for the Monti (1994) test on the lines of Katayama's correction. We show that our suggestion improves Monti's statistic in a similar way to what Katayama's suggestion does for Ljung-Box test. We also make a novel suggestion of using the pivotal portmanteau test. Our suggestion is to use two separate values of m, one a large value for the calculation of the information matrix and a smaller choice for diagnostic purposes. This results in a pivotal statistic which automatically corrects the bias correction in Ljung-Box test. Our suggested novel algorithm efciently computes this novel portmanteau test. In the second part, we implement lasso-type shrinkage methods to linear regression and time series models. We look through simulations in various examples to study the oracle properties of these methods via the adaptive lasso due to Zou (2006). We study consistent variable selection by the lasso and adaptive lasso and consider a result in the literature which states that the lasso cannot be consistent in variable selection if a necessary condition does not hold for the model. We notice that lasso methods have nice theoretical properties but it is not very easy to achieve them in practice. The choice of tuning parameter is crucial for these methods. So far there is not any fully explicit way of choosing the appropriate value of tuning parameter, so it is hard to achieve the oracle properties in practice. In our numerical study, we compare the performance of k-fold cross-validation with the BIC method of Wang et al. (2007) for selecting the appropriate value of the tuning parameter. We show that k-fold crossvalidation is not a reliable method for choosing the value of the tuning parameter for consistent variable selection. We also look at ways to implement lasso-type methods time series models. In our numerical results we show that the oracle properties of lasso-type methods can also be achieved for time series models. We derive the necessary condition for consistent variable selection by lasso-type methods in the time series context. We also prove the oracle properties of the adaptive lasso for stationary time series.
27
Carrim, Shaakira. "Power comparisons for goodness-of-fit-tests under local alternatives / S. Carrim". Thesis, North-West University, 2003. http://hdl.handle.net/10394/306.
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The bootstrap method is applied to discrete multivariate data and the power
divergence family of test statistics (PDFS). For a symmetric null hypothesis against a
local alternative, exact power values determined by Read and Cressie (1988:76-78)
are used as a basis for a comparative power study between the AE approximation of
power derived by Taneichi et al. (2002), and a bootstrap method which involves the
use of newly calculated bootstrap critical values for power calculations. Also,
traditional chi-square critical values are used to determine power for these hypotheses
and are compared with the methods mentioned above. The study focuses on small
sample sizes.Thesis (M.Sc. (Statistics))--North-West University, Potchefstroom Campus, 2004.
28
Krit, Meryam. "Goodness-of-fit tests in reliability : Weibull distribution and imperfect maintenance models". Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM038/document.
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Ce travail porte sur les tests d'adéquation en fiabilité, à la fois pour les systèmes non réparables et les systèmes réparables. Les tests d'adéquation sont des outils efficaces pour vérifier la pertinence d'un modèle pour un jeu de données. Pour les systèmes non réparables, la loi exponentielle et la loi de Weibull sont les lois de durée de vie les plus utilisées en fiabilité. Une comparaison exhaustive des tests d'adéquation pour la loi exponentielle est présentée pour des données complètes et censurées, suivie par des recommandations d'utilisation de ces tests. La loi de Weibull à deux paramètres permet de modéliser des taux de hasard décroissants et croissants contrairement à la loi exponentielle qui suppose un taux de hasard constant. Cependant, il existe moins de tests d'adéquation à la loi de Weibull dans la littérature. Une revue exhaustive des tests existant est effectuée et deux familles de tests exacts sont preésentées. La première famille est la famille des tests basés sur la vraisemblance et la deuxième est la famille des tests basés sur la transformée de Laplace. Des propriétés asymptotiques des nouvelles statistiques de tests sont établies. Une comparaison complète des tests d'adéquation pour la loi de Weibull est effectuée. Des recommandations sur les tests les plus puissants sont données en fonction des caractéristiques du jeu de donnés testé. Pour les systèmes réparables, de nouveaux tests d'adéquation sont développés pour des modèles de maintenance imparfaite avec à la fois des maintenances correctives et des maintenances préventives déterministes. Ces tests sont exacts et peuvent être appliqués à des petits jeux de données. Finalement, des applications à de vrais jeux de données issus de l'industrie sont effectuées pour des systèmes réparables et des systèmes non réparablesThis work deals with goodness-of-fit (GOF) tests in reliability for both non repairable and repairable systems. GOF tests are efficient techniques to check the relevance of a model for a given data set. For non repairable systems, the Exponential and Weibull distributions are the most used lifetimes distributions in reliability. A comprehensive comparison study of the GOF tests for the Exponential distribution is presented for complete and censored samples followed by recommendations about the use of the tests. The two-parameter Weibull distribution allows decreasing and increasing failure rates unlike the Exponential distribution that makes the assumption of a constant hazard rate. Yet, there exist less GOF tests in the literature for the Weibull distribution. A comprehensive review of the existing GOF tests is done and two new families of exact GOF tests are introduced. The first family is the likelihood based GOF tests and the second is the family of tests based on the Laplace transform. Theoretical asymptotic properties of some new tests statistics are established. A comprehensive comparison study of the GOF tests for the Weibull distribution is done. Recommendations about the most powerful tests are given depending on the characteristics of the tested data sets. For repairable systems, new GOF tests are developed for imperfect maintenance models when both corrective maintenance and deterministic preventive maintenance are performed. These tests are exact and can be applied to small data sets. Finally, illustrative applications to real data sets from industry are carried out for repairable and non repairable systems
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Taheri, Zadeh Fatemeh. "Empirical Hankel transform and statistical goodness-of-fit tests for exponential distributions". München Verl. Dr. Hut, 2009. http://d-nb.info/992892317/04.
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胡寶璇 i Pao-sun Woo. "Parametric inference for time series based upon goodness-of-fit". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31226929.
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Liang, Jia-juan. "Testing multinormality, spherical and elliptical symmetry". HKBU Institutional Repository, 1998. http://repository.hkbu.edu.hk/etd_ra/131.
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Aggarwal, Deepa. "On some inference problems for current status data". Diss., Connect to online resource - MSU authorized users, 2008.
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Thesis (Ph. D.)--Michigan State University. Dept. of Statistics and Probability, 2008.Title from PDF t.p. (viewed on July 7, 2009) Includes bibliographical references (p. 93-95). Also issued in print.
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Opperman, Logan J. "Sequential Inference and Nonparametric Goodness-of-Fit Tests for Certain Types of Skewed Distributions". Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1560856288455652.
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Tan, Falong. "Projected adaptive-to-model tests for regression models". HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/390.
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This thesis investigates Goodness-of-Fit tests for parametric regression models. With the help of sufficient dimension reduction techniques, we develop adaptive-to-model tests using projection in both the fixed dimension settings and the diverging dimension settings. The first part of the thesis develops a globally smoothing test in the fixed dimension settings for a parametric single index model. When the dimension p of covariates is larger than 1, existing empirical process-based tests either have non-tractable limiting null distributions or are not omnibus. To attack this problem, we propose a projected adaptive-to-model approach. If the null hypothesis is a parametric single index model, our method can fully utilize the dimension reduction structure under the null as if the regressors were one-dimensional. Then a martingale transformation proposed by Stute, Thies, and Zhu (1998) leads our test to be asymptotically distribution-free. Moreover, our test can automatically adapt to the underlying alternative models such that it can be omnibus and thus detect all alternative models departing from the null at the fastest possible convergence rate in hypothesis testing. A comparative simulation is conducted to check the performance of our test. We also apply our test to a self-noise mechanisms data set for illustration. The second part of the thesis proposes a globally smoothing test for parametric single-index models in the diverging dimension settings. In high dimensional data analysis, the dimension p of covariates is often large even though it may be still small compared with the sample size n. Thus we should regard p as a diverging number as n goes to infinity. With this in mind, we develop an adaptive-to-model empirical process as the basis of our test statistic, when the dimension p of covariates diverges to infinity as the sample size n tends to infinity. We also show that the martingale transformation proposed by Stute, Thies, and Zhu (1998) still work in the diverging dimension settings. The limiting distributions of the adaptive-to-model empirical process under both the null and the alternative are discussed in this new situation. Simulation examples are conducted to show the performance of this test when p grows with the sample size n. The last Chapter of the thesis considers the same problem as in the second part. Bierens's (1982) first constructed tests based on projection pursuit techniques and obtained an integrated conditional moment (ICM) test. We notice that Bierens's (1982) test performs very badly for large p, although it may be viewed as a globally smoothing test. With the help of sufficient dimension techniques, we propose an adaptive-to-model integrated conditional moment test for regression models in the diverging dimension setting. We also give the asymptotic properties of the new tests under both the null and alternative hypotheses in this new situation. When p grows with the sample size n, simulation studies show that our new tests perform much better than Bierens's (1982) original test.
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Jahan, Nusrat. "Applying goodness-of-fit techniques in testing time series Gaussianity and linearity". Diss., Mississippi State : Mississippi State University, 2006. http://sun.library.msstate.edu/ETD-db/ETD-browse/browse.
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Jansen, van Rensburg Helena Maria. "Goodness-of-fit tests based on new characterizations of the exponential distribution / Helena Maria Jansen van Rensburg". Thesis, North-West University, 2006. http://hdl.handle.net/10394/1095.
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The exponential density is probably one of the most widely used distributions in practice.
Due to its importance, many goodness-of-fit tests for exponentiality have been proposed in the
literature.
The objectives of this research are as follow:
0 to study the importance of the exponential distribution in practical problems,
0 to investigate alternative classes of distributions to the exponential distribution,
0 to present an overview of existing characterizations of the exponential distribution,
0 to evaluate existing goodness-of-fit tests for exponentiality,
0 to develop new goodness-of-fit tests for exponentiality, and
0 to compare the proposed goodness-of-fit tests to existing tests by means of relative efficiencies
and simulation studies of the power of the tests.
To achieve these objectives, we begin with a brief discussion of the exponential distribution
and other parametric families of life distributions, followed by a summary of six well-known
nonparametric classes of alternative distributions.
A comprehensive literature study of existing characterizations of the exponential distribution
and existing goodness-of fit tests for exponentiality are presented.
We then propose and prove two new characterizations of the exponential distribution in the
class of NBUE life distributions based on properties of order statistics. These characterizations
are used to develop a new class of goodness-of-fit tests for exponentiality. The tests are shown
to be consistent and the limiting distributions under the null and alternative hypotheses are
derived.
We show that the new class of test statistics includes two statistics which arc equivalent to
the well-known Gini test statistic (Gail and Gastwirth 1978a) and the coefficient of variation
test statistic (Borges, Proschan and Rodrigucs 1984).
The newly proposed tests are compared to existing goodness-of-fit tests by means of Pitman
and approximate Bahadur relative efficiencies. Monte Carlo studies are conducted to compare
the various tests with regard to power for small and moderate sample sizes against a wide range
of alternative distributions.
We recommend three members of the class of test statistics as being very effective testing
procedures for exponentiality.
In conclusion, practical examples based on real-life data are presented.Thesis (Ph.D. (Statistics))--North-West University, Potchefstroom Campus, 2007.
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Liu, Kwong Ip. "Digital net experimental designs, function interpolations using low discrepancy sequence and goodness of fit tests by discrepancy". HKBU Institutional Repository, 2007. http://repository.hkbu.edu.hk/etd_ra/807.
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Mändle, Andreas [Verfasser]. "Assessing the goodness of fit of multidimensional data – An Anderson-Darling approach to multivariate distributional tests / Andreas Mändle". München : Verlag Dr. Hut, 2016. http://d-nb.info/1097817873/34.
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Fischer, Tim [Verfasser]. "Goodness-of-fit tests for type-II right censored data : structure preserving transformations and power studies / Tim Fischer". Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2011. http://d-nb.info/1018228012/34.
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Mitchell, Dana. "Stress, Coping, and Appraisal in an HIV-seropositive Rural Sample: A Test of the Goodness-of-Fit Hypothesis". Ohio University / OhioLINK, 2004. http://www.ohiolink.edu/etd/view.cgi?ohiou1103225821.
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Bakšajev, Aleksej. "Statistical tests based on N-distances". Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100409_082443-70166.
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The thesis is devoted to the application of a new class of probability metrics, N-distances, introduced by Klebanov (Klebanov, 2005; Zinger et al., 1989), to the problems of verification of the classical statistical hypotheses of goodness of fit, homogeneity, symmetry and independence.
First of all a construction of statistics based on N metrics for testing mentioned hypotheses is proposed. Then the problem of determination of the critical region of the criteria is investigated. The main results of the thesis are connected with the asymptotic behavior of test statistics under the null and alternative hypotheses. In
general case the limit null distribution of proposed in the thesis tests statistics is established in terms of the distribution of infinite quadratic form of random normal variables with coefficients dependent on eigenvalues and functions of a certain integral operator. It is proved that under the alternative hypothesis the test statistics are asymptotically normal. In case of parametric hypothesis of goodness of fit particular attention is devoted to normality and exponentiality criteria. For hypothesis
of homogeneity a construction of multivariate distribution free two-sample test is proposed. Testing the hypothesis of uniformity on hypersphere in more detail S1 and S2 cases are investigated.
In conclusion, a comparison of N-distance tests with some classical criteria is provided. For simple hypothesis of goodness of fit in univariate case as a measure for... [to full text]Disertacinis darbas yra skirtas N-metrikų teorijos (Klebanov, 2005; Zinger et al., 1989) pritaikymui klasikinėms statistinėms suderinamumo, homogeniškumo, simetriškumo bei nepriklausomumo hipotezėms tikrinti. Darbo pradžioje pasiūlytas minėtų hipotezių testinių statistikų konstravimo būdas, naudojant N-metrikas. Toliau nagrinėjama problema susijusi su suformuotų kriterijų kritinės srities nustatymu. Pagrindiniai darbo rezultatai yra susiję su pasiūlytų kriterijaus statistikų asimptotiniu skirstiniu. Bendru atveju N-metrikos statistikų asimptotinis skirstinys esant nulinei hipotezei sutampa su Gauso atsitiktinių dydžių begalinės kvadratinės formos skirstiniu. Alternatyvos atveju testinių statistikų ribinis skirstinys yra normalusis. Sudėtinės suderinamumo hipotezės atveju išsamiau yra analizuojami normalumo ir ekponentiškumo kriterijai. Daugiamačiu atveju pasiūlyta konstrukcija, nepriklausanti nuo skirstinio homogeniškumo testo. Tikrinant tolygumo hipersferoje hipotezę detaliau yra nagrinėjami apskritimo ir sferos atvejai. Darbo pabaigoje lyginami pasiūlytos N-metrikos bei kai kurie klasikiniai kriterijai. Neparametrinės suderinamumo hipotezės vienamačiu atveju, kaip palyginimo priemonė, nagrinėjamas Bahaduro asimptotinis santykinis efektyvumas (Bahadur, 1960; Nikitin, 1995). Kartu su teoriniais rezultatais pasiūlytų N-metrikos tipo testų galingumas ištirtas, naudojant Monte-Karlo metodą. Be paprastos ir sudėtinės suderinamumo hipotezių yra analizuojami homogeniškumo testai... [toliau žr. visą tekstą]
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Zhang, Shiju. "Statistical Inferences under a semiparametric finite mixture model". See Full Text at OhioLINK ETD Center (Requires Adobe Acroba Reader for viewing), 2005. http://www.ohiolink.edu/etd/view.cgi?toledo1135779503.
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Thesis (Ph.D.)--University of Toledo, 2005.Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 100-105.
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Denson, Kathleen. "Factors Affecting Discrete-Time Survival Analysis Parameter Estimation and Model Fit Statistics". Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278405/.
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Discrete-time survival analysis as an educational research technique has focused on analysing and interpretating parameter estimates. The purpose of this study was to examine the effects of certain data characteristics on the hazard estimates and goodness of fit statistics. Fifty-four simulated data sets were crossed with four conditions in a 2 (time period) by 3 (distribution of Y = 1) by 3 (distribution of Y = 0) by 3 (sample size) design.
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Kwan, Siu Kam. "The application of measurement theory to tests in mathematics : a study of the goodness-of-fit of Rasch model to the ALIS mathematics test". Thesis, Durham University, 2003. http://etheses.dur.ac.uk/3184/.
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The scores provided by the International Test of Developed Ability (ITDA) have been used as an alternative baseline for comparing the progress of students in the A-level Information System (ALIS) project of U.K. The responses of 26,964 examinees to the mathematics items of ITDA in year 2000 were fitted by using the Rasch model. Five subject groups (the population, 2 gender groups and 2 ability groups) and 25 random samples (5 from each group) were generated from the responses of the examinees. The unconditional maximum likelihood estimates of the item difficulty and examinee ability parameters for various groups/samples were produced by the RASCAL program. The scatterplots among different sets of sample item difficulty parameters reflected that the feature of item and ability invariance was not preserved in the groups of extreme abilities. The assumptions of unidimensionality, equal item discrimination, zero guessing factor and non-speededness were generally not supported in the two ability groups. In particular, the result indicated that the ITDA Mathematical Test might be a speeded test. It was quite interesting in this study to see that the item difficulty parameters and examinee abilities estimated from the Classical Test Theory (CTT) and those from the Rasch model were very comparable and both frameworks exhibit more or less the same feature in terms of invariance. On the other hand, more items were "found" unfit by the CTT method than the Rasch approach indicating that the former looks more sensitive to the lack of fit than the latter. To study the effect of speededness, the analysis was repeated with the last 11 items (which has the highest omits) deleted. Disappointingly, the results showed no significant improvement. Further research on the fitness of data with speed incorporated into the estimation of ability level is recommended.
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Saunders, Christopher Paul. "EMPIRICAL PROCESSES FOR ESTIMATED PROJECTIONS OF MULTIVARIATE NORMAL VECTORS WITH APPLICATIONS TO E.D.F. AND CORRELATION TYPE GOODNESS OF FIT TESTS". UKnowledge, 2006. http://uknowledge.uky.edu/gradschool_diss/464.
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Goodness-of-fit and correlation tests are considered for dependent univariate data that arises when multivariate data is projected to the real line with a data-suggested linear transformation. Specifically, tests for multivariate normality are investigated. Let { } i Y be a sequence of independent k-variate normal random vectors, and let 0 d be a fixed linear transform from Rk to R . For a sequence of linear transforms { ( )} 1 , , n d Y Y converging almost surely to 0 d , the weak convergence of the empirical process of the standardized projections from d to a tight Gaussian process is established. This tight Gaussian process is identical to that which arises in the univariate case where the mean and standard deviation are estimated by the sample mean and sample standard deviation (Wood, 1975). The tight Gaussian process determines the limiting null distribution of E.D.F. goodness-of-fit statistics applied to the process of the projections. A class of tests for multivariate normality, which are based on the Shapiro-Wilk statistic and the related correlation statistics applied to the dependent univariate data that arises with a data-suggested linear transformation, is also considered. The asymptotic properties for these statistics are established. In both cases, the statistics based on random linear transformations are shown to be asymptotically equivalent to the statistics using the fixed linear transformation. The statistics based on the fixed linear transformation have same critical points as the corresponding tests of univariate normality; this allows an easy implementation of these tests for multivariate normality. Of particular interest are two classes of transforms that have been previously considered for testing multivariate normality and are special cases of the projections considered here. The first transformation, originally considered by Wood (1981), is based on a symmetric decomposition of the inverse sample covariance matrix. The asymptotic properties of these transformed empirical processes were fully developed using classical results. The second class of transforms is the principal components that arise in principal component analysis. Peterson and Stromberg (1998) suggested using these transforms with the univariate Shapiro-Wilk statistic. Using these suggested projections, the limiting distribution of the E.D.F. goodness-of-fit and correlation statistics are developed.
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Bahraoui, Tarik. "Tests de type fonction caractéristique en inférence de copules". Thèse, Université de Sherbrooke, 2017. http://hdl.handle.net/11143/11255.
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Une classe générale de statistiques de rangs basées sur la fonction caractéristique est introduite afin de tester l'hypothèse composite d'appartenance à une famille de copules multidimensionnelles. Ces statistiques d'adéquation sont définies comme des distances fonctionnelles de type L_2 pondérées entre une version non paramétrique et une version semi-paramétrique de la fonction caractéristique que l'on peut associer à une copule. Il est démontré que ces statistiques de test se comportent asymptotiquement comme des V-statistiques dégénérées d'ordre quatre et que leurs lois limites s'expriment en termes de sommes pondérées de variables khi-deux indépendantes. La convergence des tests sous des alternatives générales est établie, de même que la validité du bootstrap paramétrique pour le calcul de valeurs critiques. Le comportement des nouveaux tests sous des tailles d'échantillons faibles et modérées est étudié à l'aide de simulations et est comparé à celui d'un test concurrent fondé sur la copule empirique. La méthodologie est finalement illustrée sur un jeu de données à plusieurs dimensions.
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Tucker, Joanne M. (Joanne Morris). "Robustness of the One-Sample Kolmogorov Test to Sampling from a Finite Discrete Population". Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278186/.
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One of the most useful and best known goodness of fit test is the Kolmogorov one-sample test. The assumptions for the Kolmogorov (one-sample test) test are: 1. A random sample; 2. A continuous random variable; 3. F(x) is a completely specified hypothesized cumulative distribution function. The Kolmogorov one-sample test has a wide range of applications. Knowing the effect fromusing the test when an assumption is not met is of practical importance. The purpose of this research is to analyze the robustness of the Kolmogorov one-sample test to sampling from a finite discrete distribution. The standard tables for the Kolmogorov test are derived based on sampling from a theoretical continuous distribution. As such, the theoretical distribution is infinite. The standard tables do not include a method or adjustment factor to estimate the effect on table values for statistical experiments where the sample stems from a finite discrete distribution without replacement. This research provides an extension of the Kolmogorov test when the hypothesized distribution function is finite and discrete, and the sampling distribution is based on sampling without replacement. An investigative study has been conducted to explore possible tendencies and relationships in the distribution of Dn when sampling with and without replacement for various parameter settings. In all, 96 sampling distributions were derived. Results show the standard Kolmogorov table values are conservative, particularly when the sample sizes are small or the sample represents 10% or more of the population.
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Jaser, Miriam Angelika [Verfasser], Aleksey [Akademischer Betreuer] Min, Hajo [Gutachter] Holzmann, Yarema [Gutachter] Okhrin i Aleksey [Gutachter] Min. "Goodness-of-fit tests for elliptical copulas / Miriam Angelika Jaser ; Gutachter: Hajo Holzmann, Yarema Okhrin, Aleksey Min ; Betreuer: Aleksey Min". München : Universitätsbibliothek der TU München, 2021. http://d-nb.info/1232406260/34.
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Jin, Lei. "Generalized score tests for missing covariate data". [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1625.
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Luo, Junxiang. "Goodness-of-fit tests for proportional odds model with GEE for ordinal categorical responses & estimating sampling frequency in pollen exposure assessment over time". Cincinnati, Ohio : University of Cincinnati, 2006. http://www.ohiolink.edu/etd/view.cgi?acc%5Fnum=ucin1150094586.
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