Thèses sur le sujet « Binary model estimation »

Cette thèse s'intéresse à la résolution de problèmes inverses non linéaires exploitant un a priori de parcimonie ; plus particulièrement, des problèmes où les données se modélisent comme la combinaison linéaire d'un faible nombre de fonctions non linéaires en un paramètre dit de " localisation " (par exemple la fréquence en analyse spectrale ou le décalage temporel en déconvolution impulsionnelle). Ces problèmes se reformulent classiquement en un problème d'approximation parcimonieuse linéaire (APL) en évaluant les fonctions non linéaires sur une grille de discrétisation arbitrairement fine du paramètre de localisation, formant ainsi un " dictionnaire discret ". Cependant, une telle approche se heurte à deux difficultés majeures. D'une part, le dictionnaire provenant d'une telle discrétisation est fortement corrélé et met en échec les méthodes de résolution sous-optimales classiques comme la pénalisation L1 ou les algorithmes gloutons. D'autre part, l'estimation du paramètre de localisation, appartenant nécessairement à la grille de discrétisation, se fait de manière discrète, ce qui entraîne une erreur de modélisation. Dans ce travail nous proposons des solutions pour faire face à ces deux enjeux, d'une part via la prise en compte de la parcimonie de façon exacte en introduisant un ensemble de variables binaires, et d'autre part via la résolution " optimale " de tels problèmes sur " dictionnaire continu " permettant l'estimation continue du paramètre de localisation. Deux axes de recherches ont été suivis, et l'utilisation des algorithmes proposés est illustrée sur des problèmes de type déconvolution impulsionnelle et analyse spectrale de signaux irrégulièrement échantillonnés. Le premier axe de ce travail exploite le principe " d'interpolation de dictionnaire ", consistant en une linéarisation du dictionnaire continu pour obtenir un problème d'APL sous contraintes. L'introduction des variables binaires nous permet de reformuler ce problème sous forme de " programmation mixte en nombres entiers " (Mixed Integer Programming - MIP) et ainsi de modéliser de façon exacte la parcimonie sous la forme de la " pseudo-norme L0 ". Différents types d'interpolation de dictionnaires et de relaxation des contraintes sont étudiés afin de résoudre de façon optimale le problème grâce à des algorithmes classiques de type MIP. Le second axe se place dans le cadre probabiliste Bayésien, où les variables binaires nous permettent de modéliser la parcimonie en exploitant un modèle de type Bernoulli-Gaussien. Ce modèle est étendu (modèle BGE) pour la prise en compte de la variable de localisation continue. L'estimation des paramètres est alors effectuée à partir d'échantillons tirés avec des algorithmes de type Monte Carlo par Chaîne de Markov. Plus précisément, nous montrons que la marginalisation des amplitudes permet une accélération de l'algorithme de Gibbs dans le cas supervisé (hyperparamètres du modèle connu). De plus, nous proposons de bénéficier d'une telle marginalisation dans le cas non supervisé via une approche de type " Partially Collapsed Gibbs Sampler. " Enfin, nous avons adapté le modèle BGE et les algorithmes associés à un problème d'actualité en astrophysique : la détection d'exoplanètes par la méthode des vitesses radiales. Son efficacité sera illustrée sur des données simulées ainsi que sur des données réelles
This thesis deals with solutions of nonlinear inverse problems using a sparsity prior; more specifically when the data can be modelled as a linear combination of a few functions, which depend non-linearly on a "location" parameter, i.e. frequencies for spectral analysis or time-delay for spike train deconvolution. These problems are generally reformulated as linear sparse approximation problems, thanks to an evaluation of the nonlinear functions at location parameters discretised on a thin grid, building a "discrete dictionary". However, such an approach has two major drawbacks. On the one hand, the discrete dictionary is highly correlated; classical sub-optimal methods such as L1- penalisation or greedy algorithms can then fail. On the other hand, the estimated location parameter, which belongs to the discretisation grid, is necessarily discrete and that leads to model errors. To deal with these issues, we propose in this work an exact sparsity model, thanks to the introduction of binary variables, and an optimal solution of the problem with a "continuous dictionary" allowing a continuous estimation of the location parameter. We focus on two research axes, which we illustrate with problems such as spike train deconvolution and spectral analysis of unevenly sampled data. The first axis focusses on the "dictionary interpolation" principle, which consists in a linearisation of the continuous dictionary in order to get a constrained linear sparse approximation problem. The introduction of binary variables allows us to reformulate this problem as a "Mixed Integer Program" (MIP) and to exactly model the sparsity thanks to the "pseudo-norm L0". We study different kinds of dictionary interpolation and constraints relaxation, in order to solve the problem optimally thanks to MIP classical algorithms. For the second axis, in a Bayesian framework, the binary variables are supposed random with a Bernoulli distribution and we model the sparsity through a Bernoulli-Gaussian prior. This model is extended to take into account continuous location parameters (BGE model). We then estimate the parameters from samples drawn using Markov chain Monte Carlo algorithms. In particular, we show that marginalising the amplitudes allows us to improve the sampling of a Gibbs algorithm in a supervised case (when the model's hyperparameters are known). In an unsupervised case, we propose to take advantage of such a marginalisation through a "Partially Collapsed Gibbs Sampler." Finally, we adapt the BGE model and associated samplers to a topical science case in Astrophysics: the detection of exoplanets from radial velocity measurements. The efficiency of our method will be illustrated with simulated data, as well as actual astrophysical data

In many empirical situations, modelling simultaneously three or more outcomes as well as their dependence structure can be of considerable relevance. Trivariate modelling is continually gaining in popularity (e.g., Genest et al., 2013; Król et al., 2016; Zhong et al., 2012) because of the appealing property to account for the endogeneity issue and non-random sample selection bias, two issues that commonly arise in empirical studies (e.g., Zhang et al., 2015; Radice et al., 2013; Marra et al., 2017; Bärnighausen et al., 2011). The applied and methodological interest in trivariate modelling motivates the current thesis and the aim is to develop and estimate a generalized trivariate binary regression model, which accounts for several types of covariate effects (such as linear, nonlinear, random and spatial effects), as well as error correlations. In particular, the thesis focuses on the following targets. First, we address the issue in estimating accurately the correlation coefficients, which characterize the dependence of the binary responses conditional on regressors. We found that this is not an unusual occurrence for trivariate binary models and as far as we know such a limitation is neither discussed nor dealt with. Based on this framework, we develop models for dealing with data suffering from endogeneity and/or nonrandom sample selection. Moreover, we propose trivariate Gaussian copula models where the link functions can in principle be derived from any parametric distribution and the parameters describing the association between the responses can be made dependent on several types of covariate effects. All the coefficients of the model are estimated simultaneously within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The developments have been incorporated in the function SemiParTRIV()/gjrm() in the R package GJRM (Marra & Radice, 2017). The extensive use of simulated data as well as real datasets illustrates each development in detail and completes the analysis.

This thesis studies the one-factor latent trait model for binary data. In examines the sensitivity of the model when the assumptions about the model are violated, it investigates the information about the prior distribution when the model is estimated semi-parametrically and it also examines the goodness-of-fit of the model using Monte-Carlo simulations. Latent trait models are applied to data arising from psychometric tests, ability tests or attitude surveys. The data are often contaminated by guessing, cheating, unwillingness to give the true answer or gross errors. To study the sensitivity of the model when the data are contaminated we derive the Influence Function of the parameters and the posterior means, a tool developed in the frame of robust statistics theory. We study the behaviour of the Influence Function for changes in the data and also the behaviour of the parameters and the posterior means when the data are artificially contaminated. We further derive the Influence Function of the parameters and the posterior means for changes in the prior distribution and study empirically the behaviour of the model when the prior is a mixture of distributions. Semiparametric estimation involves estimation of the prior together with the item parameters. A new algorithm for fully semiparametric estimation of the model is given. The bootstrap is then used to study the information on the latent distribution than can be extracted from the data when the model is estimated semiparametrically. The use of the usual goodness-of-fit statistics has been hampered for latent trait models because of the sparseness of the tables. We propose the use of Monte-Carlo simulations to derive the empirical distribution of the goodness-of-fit statistics and also the examination of the residuals as they may pinpoint to the sources of bad fit.

The most common analysis used for binary data is generalised linear model (GLM) with either a binomial or bernoulli distribution using either a logit, probit, complementary log-log or other type of link functions. However, such analyses violate the independence assumption if the binary data are measured repeatedly over time at the same subject or site. Failure to take into account the correlation can lead to incorrect estimation of regression parameters and the estimates are less efficient, particularly when the correlations are large. Therefore, to obtain the most efficient estimates that are also unbiased the methods that incorporate correlations (McCullagh and Nelder, 1989) should be used. Two of the statistical methodologies that can be used to account for this correlation for the longitudinal data are the generalized linear mixed models (GLMMs) and generalized estimating equation (GEE). The GLMM method is based on extending the fixed effects GLM to include random effects and covariance patterns. Unlike the GLM and GLMM methods, the GEE method is based on the quasi-likelihood theory and no assumption is made about the distribution of response observations (Liang and Zeger, 1986). The main objective of the study is to investigate the statistical properties and limitations of these three approaches, i.e. GLM, GLMMs and GEE for analyzing longitudinal data through use of a binary data from an entomology study. The results reaffirms the point made by these authors that misspecification of working correlation in GEE approach would still give consistent regression parameter estimates. Further, the results of this study suggest that even with small correlation, ignoring a random effects in a binary model can lead to inconsistent estimation.
Dissertation (MSc)--University of Pretoria, 2014.
lk2014
Statistics
MSc
Unrestricted

Longitudinal data arise when subjects are followed over time. This type of data is typically dependent, due to including repeated observations and this type of dependence is termed as within-subject dependence. Often the scientific interest is on multiple longitudinal measurements which introduce two additional types of associations, between-response and cross-response temporal dependencies. Only the statistical methods which take these association structures might yield reliable and valid statistical inferences. Although the methods for univariate longitudinal data have been mostly studied, multivariate longitudinal data still needs more work. In this thesis, although we mainly focus on multivariate longitudinal binary data models, we also consider other types of response families when necessary. We extend a work on multivariate marginal models, namely multivariate marginal models with response specific parameters (MMM1), and propose multivariate marginal models with shared regression parameters (MMM2). Both of these models are generalized estimating equation (GEE) based, and are valid for several response families such as Binomial, Gaussian, Poisson, and Gamma. Two different R packages, mmm and mmm2 are proposed to fit them, respectively. We further develop a marginalized multilevel model, namely probit normal marginalized transition random effects models (PNMTREM) for multivariate longitudinal binary response. By this model, implicit function theorem is introduced to explicitly link the levels of marginalized multilevel models with transition structures for the first time. An R package, bf pnmtrem is proposed to fit the model. PNMTREM is applied to data collected through Iowa Youth and Families Project (IYFP). Five different models, including univariate and multivariate ones, are considered to forecast multivariate longitudinal binary data. A comparative simulation study, which includes a model-independent data simulation process, is considered for this purpose. Forecasting independent variables are taken into account as well. To assess the forecasts, several accuracy measures, such as expected proportion of correct prediction (ePCP), area under the receiver operating characteristic (AUROC) curve, mean absolute scaled error (MASE) are considered. Mother'
s Stress and Children'
s Morbidity (MSCM) data are used to illustrate this comparison in real life. Results show that marginalized models yield better forecasting results compared to marginal models. Simulation results are in agreement with these results as well.

In this study, we use a hazard-based modeling as an alternative statistical framework to time series methods as applied to climate data. Data collected from the Kentucky Mesonet will be used to study the distributional properties of the duration of high and low-energy wind events relative to an arbitrary threshold. Our objectiveswere to fit bathtub models proposed in literature, propose a generalized bathtub model, apply these models to Kentucky Mesonet data, and make recommendations as to feasibility of wind power generation. Using two different thresholds (1.8 and 10 mph respectively), results show that the Hjorth bathtub model consistently performed better than all other models considered with coefficient of R-squared values at 0.95 or higher. However, fewer sites and months could be included in the analysis when we increased our threshold to 10 mph. Based on a 10 mph threshold, Bowling Green (FARM), Hopkinsville (PGHL), and Columbia (CMBA) posted the top 3 wind duration times in February of 2009. Further studies needed to establish long-term trends.

Ce mémoire de thèse porte sur la statistique inférentielle des données spatiales et/ou fonctionnelles. En effet, nous nous sommes intéressés à l’estimation de paramètres inconnus de certains modèles à partir d’échantillons obtenus par un processus d’échantillonnage aléatoire ou non (stratifié), composés de variables indépendantes ou spatialement dépendantes.La spécificité des méthodes proposées réside dans le fait qu’elles tiennent compte de la nature de l’échantillon étudié (échantillon stratifié ou composé de données spatiales dépendantes).Tout d’abord, nous étudions des données à valeurs dans un espace de dimension infinie ou dites ”données fonctionnelles”. Dans un premier temps, nous étudions les modèles de choix binaires fonctionnels dans un contexte d’échantillonnage par stratification endogène (échantillonnage Cas-Témoin ou échantillonnage basé sur le choix). La spécificité de cette étude réside sur le fait que la méthode proposée prend en considération le schéma d’échantillonnage. Nous décrivons une fonction de vraisemblance conditionnelle sous l’échantillonnage considérée et une stratégie de réduction de dimension afin d’introduire une estimation du modèle par vraisemblance conditionnelle. Nous étudions les propriétés asymptotiques des estimateurs proposées ainsi que leurs applications à des données simulées et réelles. Nous nous sommes ensuite intéressés à un modèle linéaire fonctionnel spatial auto-régressif. La particularité du modèle réside dans la nature fonctionnelle de la variable explicative et la structure de la dépendance spatiale des variables de l’échantillon considéré. La procédure d’estimation que nous proposons consiste à réduire la dimension infinie de la variable explicative fonctionnelle et à maximiser une quasi-vraisemblance associée au modèle. Nous établissons la consistance, la normalité asymptotique et les performances numériques des estimateurs proposés.Dans la deuxième partie du mémoire, nous abordons des problèmes de régression et prédiction de variables dépendantes à valeurs réelles. Nous commençons par généraliser la méthode de k-plus proches voisins (k-nearest neighbors; k-NN) afin de prédire un processus spatial en des sites non-observés, en présence de co-variables spatiaux. La spécificité du prédicteur proposé est qu’il tient compte d’une hétérogénéité au niveau de la co-variable utilisée. Nous établissons la convergence presque complète avec vitesse du prédicteur et donnons des résultats numériques à l’aide de données simulées et environnementales.Nous généralisons ensuite le modèle probit partiellement linéaire pour données indépendantes à des données spatiales. Nous utilisons un processus spatial linéaire pour modéliser les perturbations du processus considéré, permettant ainsi plus de flexibilité et d’englober plusieurs types de dépendances spatiales. Nous proposons une approche d’estimation semi paramétrique basée sur une vraisemblance pondérée et la méthode des moments généralisées et en étudions les propriétés asymptotiques et performances numériques. Une étude sur la détection des facteurs de risque de cancer VADS (voies aéro-digestives supérieures)dans la région Nord de France à l’aide de modèles spatiaux à choix binaire termine notre contribution
This thesis is about statistical inference for spatial and/or functional data. Indeed, weare interested in estimation of unknown parameters of some models from random or nonrandom(stratified) samples composed of independent or spatially dependent variables.The specificity of the proposed methods lies in the fact that they take into considerationthe considered sample nature (stratified or spatial sample).We begin by studying data valued in a space of infinite dimension or so-called ”functionaldata”. First, we study a functional binary choice model explored in a case-controlor choice-based sample design context. The specificity of this study is that the proposedmethod takes into account the sampling scheme. We describe a conditional likelihoodfunction under the sampling distribution and a reduction of dimension strategy to definea feasible conditional maximum likelihood estimator of the model. Asymptotic propertiesof the proposed estimates as well as their application to simulated and real data are given.Secondly, we explore a functional linear autoregressive spatial model whose particularityis on the functional nature of the explanatory variable and the structure of the spatialdependence. The estimation procedure consists of reducing the infinite dimension of thefunctional variable and maximizing a quasi-likelihood function. We establish the consistencyand asymptotic normality of the estimator. The usefulness of the methodology isillustrated via simulations and an application to some real data.In the second part of the thesis, we address some estimation and prediction problemsof real random spatial variables. We start by generalizing the k-nearest neighbors method,namely k-NN, to predict a spatial process at non-observed locations using some covariates.The specificity of the proposed k-NN predictor lies in the fact that it is flexible and allowsa number of heterogeneity in the covariate. We establish the almost complete convergencewith rates of the spatial predictor whose performance is ensured by an application oversimulated and environmental data. In addition, we generalize the partially linear probitmodel of independent data to the spatial case. We use a linear process for disturbancesallowing various spatial dependencies and propose a semiparametric estimation approachbased on weighted likelihood and generalized method of moments methods. We establishthe consistency and asymptotic distribution of the proposed estimators and investigate thefinite sample performance of the estimators on simulated data. We end by an applicationof spatial binary choice models to identify UADT (Upper aerodigestive tract) cancer riskfactors in the north region of France which displays the highest rates of such cancerincidence and mortality of the country

With the recent innovations in technology, sports betting became more accessible to any bettor, professional or not. An analysis of tennis and models applicable on the estimation of the result of men’s tennis matches in Grand Slam tournaments allowed us to identify a model with the capacity to predict the result with a 76,02% accuracy. The selected model was applied on a case study, using Betfair as an example of an ‘exchange’ platform. This approach allows us to compare the estimated odds and the odds present at the betting market in such a way that the predictive ability of the model is assessed. Further developments are suggested in the conclusion; Resumo: Negociação interativa pré-jogo no mercado de apostas de ténis: probabilidade de ganhar um jogo em torneios do Grand Slam Com os mais recentes avanços tecnológicos, a aposta desportiva tornou-se acessível para qualquer tipo de apostador, quer amador, quer profissional. Uma análise ao caso específico do ténis, baseada na aplicação de modelos para resposta binária ao resultado de um jogo de ténis masculino durante o torneio do Grand Slam, permitiu-nos identificar um modelo com a capacidade de prever o resultado para 76,02% dos jogos. O modelo seleccionado foi aplicado num estudo de caso, usando Betfair como exemplo de uma plataforma de apostas. O modelo permite-nos comparar as probabilidades estimadas e as probabilidades existentes no mercado de apostas, e identificar se a previsão do resultado de um determinado jogo vai ao encontro das expectativas do mercado. Desenvolvimentos adicionais são sugeridos na conclusão.

This thesis consists of three papers that makes independent contributions to the fields of forecast evaluation and financial econometrics. As such, the papers, chapter 1-3, can be read independently of each other. In Chapter 1, “Inferring an agent’s loss function based on a term structure of forecasts”, we provide conditions for identification, estimation and inference of an agent’s loss function based on an observed term structure of point forecasts. The loss function specification is flexible as we allow the preferences to be both asymmetric and to vary non-linearly across the forecast horizon. In addition, we introduce a novel forecast rationality test based on the estimated loss function. We employ the approach to analyse the U.S. Government’s preferences over budget surplus forecast errors. Interestingly, we find that it is relatively more costly for the government to underestimate the budget surplus and that this asymmetry is stronger at long forecast horizons. In Chapter 2, “Monitoring Systemic Risk”, we define systemic risk as the conditional probability of a systemic banking crisis. This conditional probability is modelled in a fixed effect binary response panel-model framework that allows for cross-sectional dependence (e.g. due to contagion effects). In the empirical application we identify several risk factors and it is shown that the level of systemic risk contains a predictable component which varies through time. Furthermore, we illustrate how the forecasts of systemic risk map into dynamic policy thresholds in this framework. Finally, by conducting a pseudo out-of-sample exercise we find that the systemic risk estimates provided reliable early-warning signals ahead of the recent financial crisis for several economies. Finally, in Chapter 3, “Equity Premium Predictability”, we reassess the evidence of out-of- sample equity premium predictability. The empirical finance literature has identified several financial variables that appear to predict the equity premium in-sample. However, Welch & Goyal (2008) find that none of these variables have any predictive power out-of-sample. We show that the equity premium is predictable out-of-sample once you impose certain shrinkage restrictions on the model parameters. The approach is motivated by the observation that many of the proposed financial variables can be characterised as ’weak predictors’ and this suggest that a James-Stein type estimator will provide a substantial risk reduction. The out-of-sample explanatory power is small, but we show that it is, in fact, economically meaningful to an investor with time-invariant risk aversion. Using a shrinkage decomposition we also show that standard combination forecast techniques tends to ’overshrink’ the model parameters leading to suboptimal model forecasts.

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The objective of this work is to present techniques of regression analysis for longitudinal data when the response variable is binary. Initially, there is a review of generalized linear models, marginal models, transition models, mixed models, and logistic regression methods of estimation, which will be necessary for the development of work. In addition to the methods of estimation, some structures of correlation will be studied in an attempt to capture the intra-individual serial dependence over time. These methods were applied in two situations, one where the response variable is continuous and normal distribution, and another when the response variable has the Bernoulli distribution. It was also sought to explore and present techniques for selection of models and diagnostics for the two cases. Finally, an application of the above methodology will be presented using a set of real data.
O objetivo deste trabalho é apresentar técnicas de análise de regressão para dados longitudinais quando a variável resposta é binária. Inicialmente, é feita uma revisão sobre modelos lineares generalizados, modelos marginais, modelos de transição, modelos mistos, regressão logística e métodos de estimação, pois serão necessários para o desenvolvimento do trabalho. Além dos métodos de estimação, algumas estruturas de correlação serão estudadas, na tentativa de captar a dependência serial intra-indivíduo ao longo do tempo. Estes métodos foram aplicados em duas situações; uma quando a variável resposta é contínua, e se assume ter distribuição normal, e a outra quando a variável resposta assume ter distribuição de Bernoulli. Também se procurou pesquisar e apresentar técnicas de seleção de modelos e de diagnósticos para os dois casos. Ao final, uma aplicação com a metodologia pesquisada será apresentada utilizando um conjunto de dados reais.

碩士
國立中正大學
國際經濟研究所
89
Abstract Binary choice model has been widely used in analysis of a single dependent variable that is observed as a dichotomous value. In the thesis, we focus on the rank-based estimations of binary choice model. The conclusive objectives are as follows: Ⅰ. Introduce the rank-based estimation of the slope parameters in the binary choice model: maximum rank correlation (MRC) estimator. Ⅱ. Impose the rank-based estimation of location parameter in the binary choice model. Ⅲ. Compare with other research which is based on parametric estimation in binary choice model by using the Monte Carlo simulation and an empirical study to illustrate the differences between parametric and non-parametric estimation since the MRC estimator is non-parametric with respect to the model structure and non-parametric with respect to the error term.

碩士
國立中山大學
應用數學系研究所
93
This paper is concerned with the problem of finding an experimental design for discrimination between two rival models and for model robustness that minimizing the maximum bias simultaneously in binary response experiments. The criterion for model discrimination is based on the $T$-optimality criterion proposed in Atkinson and Fedorov (1975), which maximizes the sum of squares of deviations between the two rival models while the criterion for model robustness is based on minimizing the maximum probability bias of the two rival models. In this paper we obtain the optimum designs satisfy the above two criteria for some commonly used rival models in binary response experiments such as the probit and logit models etc.

La tesi analizza la letteratura sugli effetti del sistema fiscale sulle decisioni finanziarie e di investimento delle imprese. Viene stimato l'effetto di una serie di variabili di lbilancio sulla probabilità di investimento delle imprese su una banca dati di bilanci di imprese.

In his theory of General Relativity, Einstein describes gravity as a geometric property of spacetime, which deforms in the presence of mass and energy. The accelerated motion of masses produces deformations, which propagate outward from their source at the speed of light. We refer to these radiated deformations as gravitational waves. Over the past several decades, the goal of the Laser Interferometer Gravitational-wave Observatory (LIGO) has been the search for direct evidence of gravitational waves from astrophysical sources, using ground based laser interferometers. As LIGO moves into its Advanced era (aLIGO), the direct detection of gravitational waves is inevitable. With the technology at hand, it is imperative that we have the tools to analyze the detector signal and examine the interesting astrophysical properties of the source. Some of the main targets of this search are coalescing compact binaries. In this thesis, I describe and evaluate bhextractor, a data analysis algorithm that uses Principal Component Analysis (PCA) to identify the main features of a set of gravitational waveforms produced by the coalescence of two black holes. Binary Black Hole (BBH) systems are expected to be among the most common sources of gravitational waves in the sensitivity band of aLIGO. However, the gravitational waveforms emitted by BBH systems are not well modeled and require computationally expensive Numerical Relativity (NR) simulations. bhextractor uses PCA to decompose a catalog of available NR waveforms into a set of orthogonal Principal Components (PCs), which efficiently select the major common features of the waveforms in the catalog and represent a portion of the BBH parameter space. From these PCs, we can reconstruct any waveform in the catalog, and construct new waveforms with similar properties. Using Bayesian analysis and Nested Sampling, one can use bhextractor to classify an arbitrary BBH waveform into one of the available catalogs and estimate the parameters of the gravitational wave source.

The predictability of excess stock returns has been debated by researchers over time, with many studies proving that stock returns can be predicted to some extent. To enable an effective investment strategy, it is vital for investors to identify the future directions of stock returns and the factors causing directional changes. This study sought to determine whether Australian monthly excess stock return signs are predictable, and identify the key determinants of Australian monthly excess stock return directions. Three different binary models were considered to predict stock directions: discriminant, logistic and probit models. The predictive powers of benchmark static logistic and probit models were also compared with dynamic, autoregressive and dynamic autoregressive models. In order to identify the key determinants, this study considered various economic, international and financial factors, as well as past volatility measures of explanatory variables. It also tested a United States (US) binary recession indicator and Organisation for Economic Co-operation and Development (OECD) composite leading indicator as explanatory variables in the predictive models.

This thesis proposes a new estimator, namely, a weighted semiparametric estimator (WSPE) for binary response models incorporating both the probit and single index model (SIM). Appropriate weights for the probit and SIM are estimated via bayesian model averaging (BMA). The assigned weights are proportional to the information obtained from maximum likelihood (ML) values of the SIM and the probit, respectively; these ML values are then used to calculate the marginal likelihood in the BMA. The finite sample performance of the WSPE is compared to the performance of the probit and SIM. Simulation results of this research show that the WSPE achieves significant bias reduction and up to 46% gain in efficiency. The results of the empirical application show that the WSPE performs as well as the probit when the data meets the probit assumptions, and as well as the SIM otherwise.

碩士
國立彰化師範大學
統計資訊研究所
97
In clinical studies, we usually concern agreement between different raters or methods. The kappa statistic is the most popular index for assessing agreement of categorical or ordinal outcomes. In this thesis, we propose the generalized estimating equation (GEE) approach to estimate kappa measures on inter and intra agreement for correlated dichotomous data and test the equality of the several dependent kappa coefficients. In addition, we apply the quasi-likelihood under the independence model criterion (QIC) measures and Pearson  2 statistics for model selection. Simulation studies are conducted to evaluate the performance of GEE under each model-selection criterion. We conclude that model selection is a crucial step before making inference with kappa estimates. Analyses of two studies of repeated binary ratings are used for illustration.

Chan, Chun Lam.
Thesis M.Phil. Chinese University of Hong Kong 2015.
Includes bibliographical references (leaves 74-78).
Abstracts also in Chinese.
Title from PDF title page (viewed on 19, September, 2016).

In some situations we cannot observe the original time series and instead, we record only binary data which express whether the values of the original series exceeded a certain threshold or not. The thesis deals with estimation of characteristics of the original series constructed from the binary (so called clipped or hard-limited) data, in particular in Gaussian ARMA models. We summarize some basic characteristics of the clipped series and describe their relation to the original ones. Some practical examples are provided as well. The estimation of parameters in AR(p) model is shown for the case of zero threshold. Using a similar approach, an estimator of the MA(1) model parameter is proposed and its properties are studied with emphasis on asymptotic variance. Subsequently, we propose an estimation procedure for AR(p) and MA(1) models with unknown (non-zero) threshold. The behaviour of our estimators is investigated in a simulation study, which provides a comparison with estimators constructed from the original data. Finally, a real data analysis is presented for an illustration. Powered by TCPDF (www.tcpdf.org)

碩士
國立中山大學
應用數學系
87
In Chapter 1, we consider D-, A- and Ds-optimal design problems in linear regression models with a one-dimensional control variable and k-dimensional response variable Y=(Y1,...,Yk) which have some common parameters. The D- and Ds-optimal designs obtained are independent of the covariance structure. The A-optimal designs in some low degree cases are also found explicitly which depend on the covariance structure. In Chapter 2, we consider model robust design criterion for estimating extreme quantiles in binary response experiment if there is uncertainly on the true model. We find the model robust optimal designs are very efficient for the cases studied. We also propose quantile robust design criterion as well as model and quantile robust design criterion, and examples are given to illustrate use of these criteria.

Multiple-outcome longitudinal data are abundant in clinical investigations. For example, infections with different pathogenic organisms are often tested concurrently, and assessments are usually taken repeatedly over time. It is therefore natural to consider a multivariate modeling approach to accommodate the underlying interrelationship among the multiple longitudinally measured outcomes. This dissertation proposes a multivariate semiparametric modeling framework for such data. Relevant estimation and inference procedures as well as model selection tools are discussed within this modeling framework. The first part of this research focuses on the analytical issues concerning binary data. The second part extends the binary model to a more general situation for data from the exponential family of distributions. The proposed model accounts for the correlations across the outcomes as well as the temporal dependency among the repeated measures of each outcome within an individual. An important feature of the proposed model is the addition of a bivariate smooth function for the depiction of concurrent nonlinear and possibly interacting influences of two independent variables on each outcome. For model implementation, a general approach for parameter estimation is developed by using the maximum penalized likelihood method. For statistical inference, a likelihood-based resampling procedure is proposed to compare the bivariate nonlinear effect surfaces across the outcomes. The final part of the dissertation presents a variable selection tool to facilitate model development in practical data analysis. Using the adaptive least absolute shrinkage and selection operator (LASSO) penalty, the variable selection tool simultaneously identifies important fixed effects and random effects, determines the correlation structure of the outcomes, and selects the interaction effects in the bivariate smooth functions. Model selection and estimation are performed through a two-stage procedure based on an expectation-maximization (EM) algorithm. Simulation studies are conducted to evaluate the performance of the proposed methods. The utility of the methods is demonstrated through several clinical applications.