Orientador: Víctor Hugo Lachos Dávila / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:55:07Z (GMT). No. of bitstreams: 1 Massuia_MoniqueBettio_M.pdf: 2926597 bytes, checksum: 2a1154c0a61b13f369e8390159fc4c3e (MD5) Previous issue date: 2015 / Resumo: Este trabalho tem como objetivo principal apresentar os modelos de regressão lineares com respostas censuradas sob a classe de distribuições de mistura de escala skew-normal (SMSN), visando generalizar o clássico modelo Tobit ao oferecer alternativas mais robustas à distribuição Normal. Um estudo de inferência clássico é desenvolvido para os modelos em questão sob dois casos especiais desta família de distribuições, a Normal e a t de Student, utilizando o algoritmo EM para obter as estimativas de máxima verossimilhança dos parâmetros dos modelos e desenvolvendo métodos de diagnóstico de influência global e local com base na metodologia proposta por Cook (1986) e Poom & Poon (1999). Sob o enfoque Bayesiano, o modelo de regressão para respostas censuradas é estudado sob alguns casos especiais da classe SMSN, como a Normal, a t de Student, a skew-Normal, a skew-t e a skew-Slash. Neste caso, o amostrador de Gibbs é a principal ferramenta utilizada para a inferência sobre os parâmetros do modelo. Apresentamos também alguns estudos de simulação para avaliar a metodologia desenvolvida que, por fim, é aplicada em dois conjuntos de dados reais. Os pacotes SMNCensReg, CensRegMod e BayesCR para o software R dão suporte computacional aos desenvolvimentos deste trabalho / Abstract: This work aims to present the linear regression model with censored response variable under the class of scale mixture of skew-normal distributions (SMSN), generalizing the well known Tobit model as providing a more robust alternative to the normal distribution. A study based on classic inference is developed to investigate these censored models under two special cases of this family of distributions, Normal and t-Student, using the EM algorithm for obtaining maximum likelihood estimates and developing methods of diagnostic based on global and local influence as suggested by Cook (1986) and Poom & Poon (1999). Under a Bayesian approach, the censored regression model was studied under some special cases of SMSN class, such as Normal, t-Student, skew-Normal, skew-t and skew-Slash. In these cases, the Gibbs sampler was the main tool used to make inference about the model parameters. We also present some simulation studies for evaluating the developed methodologies that, finally, are applied on two real data sets. The packages SMNCensReg, CensRegMod and BayesCR implemented for the software R give computational support to this work / Mestrado / Estatistica / Mestra em Estatística

This dissertation consists of four independent but related parts, each in a Chapter. The first part is an introductory. It serves as the background introduction and offer preparations for later parts. The second part discusses two population multivariate normal distributions with common covariance matrix. The goal for this part is to derive objective/non-informative priors for the parameterizations and use these priors to build up constructive random posteriors of the Kullback-Liebler (KL) divergence of the two multivariate normal populations, which is proportional to the distance between the two means, weighted by the common precision matrix. We use the Cholesky decomposition for re-parameterization of the precision matrix. The KL divergence is a true distance measurement for divergence between the two multivariate normal populations with common covariance matrix. Frequentist properties of the Bayesian procedure using these objective priors are studied through analytical and numerical tools. The third part considers the star-shape Gaussian graphical model, which is a special case of undirected Gaussian graphical models. It is a multivariate normal distribution where the variables are grouped into one "global" group of variable set and several "local" groups of variable set. When conditioned on the global variable set, the local variable sets are independent of each other. We adopt the Cholesky decomposition for re-parametrization of precision matrix and derive Jeffreys' prior, reference prior, and invariant priors for new parameterizations. The frequentist properties of the Bayesian procedure using these objective priors are also studied. The last part concentrates on the discussion of objective Bayesian analysis for partial correlation coefficient and its application to multivariate Gaussian models. / Ph. D.

A presente tese aborda aspectos teóricos e aplicados da estimação dos parâmetros do modelo de calibração linear com erros distribuídos conforme a distribuição normal-assimétrica (Azzalini, 1985) e t-normal-assimétrica (Gómez, Venegas e Bolfarine, 2007). Aplicando um modelo assimétrico, não é necessário transformar as variáveis a fim de obter erros simétricos. A estimação dos parâmetros e das variâncias dos estimadores do modelo de calibração foram estudadas através da visão freqüentista e bayesiana, desenvolvendo algoritmos tipo EM e amostradores de Gibbs, respectivamente. Um dos pontos relevantes do trabalho, na óptica freqüentista, é a apresentação de uma reparametrização para evitar a singularidade da matriz de informação de Fisher sob o modelo de calibração normal-assimétrico na vizinhança de lambda = 0. Outro interessante aspecto é que a reparametrização não modifica o parâmetro de interesse. Já na óptica bayesiana, o ponto forte do trabalho está no desenvolvimento de medidas para verificar a qualidade do ajuste e que levam em consideração a assimetria do conjunto de dados. São propostas duas medidas para medir a qualidade do ajuste: o ADIC (Asymmetric Deviance Information Criterion) e o EDIC (Evident Deviance Information Criterion), que são extensões da ideia de Spiegelhalter et al. (2002) que propôs o DIC ordinário que só deve ser usado em modelos simétricos. / This thesis focuses on theoretical and applied estimation aspects of the linear calibration model with skew-normal (Azzalini, 1985) and skew-t-normal (Gómez, Venegas e Bolfarine, 2007) error distributions. Applying the asymmetrical distributed error methodology, it is not necessary to transform the variables in order to have symmetrical errors. The frequentist and the Bayesian solution are presented. The parameter estimation and its variance estimation were studied using the EM algorithm and the Gibbs sampler, respectively, in each approach. The main point, in the frequentist approach, is the presentation of a new parameterization to avoid singularity of the information matrix under the skew-normal calibration model in a neighborhood of lambda = 0. Another interesting aspect is that the reparameterization developed to make the information matrix nonsingular, when the skewness parameter is near to zero, leaves the parameter of interest unchanged. The main point, in the Bayesian framework, is the presentation of two measures of goodness-of-fit: ADIC (Asymmetric Deviance Information Criterion) and EDIC (Evident Deviance Information Criterion ). They are natural extensions of the ordinary DIC developed by Spiegelhalter et al. (2002).

A presente tese aborda aspectos teóricos e aplicados da estimação dos parâmetros do modelo de calibração linear com erros distribuídos conforme a distribuição normal-assimétrica (Azzalini, 1985) e t-normal-assimétrica (Gómez, Venegas e Bolfarine, 2007). Aplicando um modelo assimétrico, não é necessário transformar as variáveis a fim de obter erros simétricos. A estimação dos parâmetros e das variâncias dos estimadores do modelo de calibração foram estudadas através da visão freqüentista e bayesiana, desenvolvendo algoritmos tipo EM e amostradores de Gibbs, respectivamente. Um dos pontos relevantes do trabalho, na óptica freqüentista, é a apresentação de uma reparametrização para evitar a singularidade da matriz de informação de Fisher sob o modelo de calibração normal-assimétrico na vizinhança de lambda = 0. Outro interessante aspecto é que a reparametrização não modifica o parâmetro de interesse. Já na óptica bayesiana, o ponto forte do trabalho está no desenvolvimento de medidas para verificar a qualidade do ajuste e que levam em consideração a assimetria do conjunto de dados. São propostas duas medidas para medir a qualidade do ajuste: o ADIC (Asymmetric Deviance Information Criterion) e o EDIC (Evident Deviance Information Criterion), que são extensões da ideia de Spiegelhalter et al. (2002) que propôs o DIC ordinário que só deve ser usado em modelos simétricos. / This thesis focuses on theoretical and applied estimation aspects of the linear calibration model with skew-normal (Azzalini, 1985) and skew-t-normal (Gómez, Venegas e Bolfarine, 2007) error distributions. Applying the asymmetrical distributed error methodology, it is not necessary to transform the variables in order to have symmetrical errors. The frequentist and the Bayesian solution are presented. The parameter estimation and its variance estimation were studied using the EM algorithm and the Gibbs sampler, respectively, in each approach. The main point, in the frequentist approach, is the presentation of a new parameterization to avoid singularity of the information matrix under the skew-normal calibration model in a neighborhood of lambda = 0. Another interesting aspect is that the reparameterization developed to make the information matrix nonsingular, when the skewness parameter is near to zero, leaves the parameter of interest unchanged. The main point, in the Bayesian framework, is the presentation of two measures of goodness-of-fit: ADIC (Asymmetric Deviance Information Criterion) and EDIC (Evident Deviance Information Criterion ). They are natural extensions of the ordinary DIC developed by Spiegelhalter et al. (2002).

The use of distributed systems, involving multiple components, has become a common industry practice. However, modeling the behaviour of such systems is a challenge, especially when the behavior consists of several collaborations of different parties, each involving possibly several starting (input) and ending (output) events of the involved components. Furthermore, the global behavior should be described as a composition of several sub-behaviours, in the following called collaborations, and each collaboration may be further decomposed into several sub-collaborations. We assume that the performance of the elementary sub-collaborations is known, and that the performance of the global behavior should be determined from the performance of the contained elementary collaborations and the form of the composition. A collaboration, in this thesis, is characterized by a partial order of input and output events, and the performance of the collaboration is defined by the minimum delays required for a given output event with respect to an input event. This is a generalization of the semantics of UML Activities, where all input events are assumed to occur at the same time, and all output events occur at the same time. We give a semantic definition of the dynamic behavior of composed collaborations using the composition operators for control flow from UML Activity diagrams, in terms of partial order relationships among the involved input and output events. Based on these semantics, we provide formulas for calculating the performance of composed collaborations in terms of the performance of the sub-collaborations, where each delay is characterized by (a) a fixed value, (b) a range of values, and (c) a distribution (in the case of stochastic behaviours). We also propose approximations for the case of stochastic behavior with Normal distributions, and discuss the expected errors that may be introduced due to ignoring of shared resources or possible dependencies in the case of stochastic behaviours. A tool has been developed for evaluating the performance of complex collaborations, and examples and case studies are discussed to illustrate the applicability of the performance analysis and the visual notation which we introduced for representing the partial-order relationships of the input and output events.

Made available in DSpace on 2016-06-02T20:05:59Z (GMT). No. of bitstreams: 1 DissANCP.pdf: 696592 bytes, checksum: 1733e6a92a2421365932309fcb98d372 (MD5) Previous issue date: 2007-04-20 / The Item Response Theory (IRT) is a set of mathematical models representing the probability of an individual to take a correct response of an item and its ability. The purpose of our research is to show the models formulated in the IRT under the skew-normal distributions and to develop flexible alternative models. With this goal in mind we introduced the t-skew distributions (Azzalini et al. 1999) and results similar to Bazan s results are obtained. Some applications using Bayesian methods are also considered. / A Teoria de Resposta ao Item (TRI) e um conjunto de modelos matematicos que representam a probabilidade de um indivıduo dar uma resposta certa a um item (questao) como funcao dos parametros do item e da habilidade do indivıduo. O objetivo de nossa pesquisa e apresentar os modelos propostos na TRI normal assimetrica e desenvolver modelos alternativos mais flexıveis. Com esta finalidade em mente, introduzimos a distribuicao t-assimetrica (Azzalini e Capitanio 1999) e obtemos resultados similares aos obtidos por Bazan (2005). Algumas aplicacoes utilizando metodos bayesianos sao consideradas.

Orientadores: Victor Hugo Lachos Dávila, Filidor Edilfonso Vilca Labra / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T04:06:26Z (GMT). No. of bitstreams: 1 MedinaGaray_AldoWilliam_M.pdf: 1389516 bytes, checksum: 2763869ea52e11ede3c860714ea0e75e (MD5) Previous issue date: 2010 / Resumo: Neste trabalho estudamos alguns aspectos de estimação e diagnóstico de influência global e local de modelos não lineares sob a classe de distribuição misturas da escala skew-normal, baseado na metodologia proposta por Cook (1986) e Poon & Poon (1999). Os modelos não lineares heteroscedásticos também são discutidos. Esta nova classe de modelos constitui uma generalização robusta dos modelos de regressão não linear simétricos, que têm como membros particulares distribuições com caudas pesadas, tais como skew-t, skew-slash, skew-normal contaminada, entre outras. A estimação dos parâmetros será obtida via o algoritmo EM proposto por Dempster et al. (1977). Estudos de testes de hipóteses são considerados utilizando as estatísticas de escore e da razão de verossimilhança, para testar a homogeneidade do parâmetro de escala. Propriedades das estatísticas do teste são investigadas através de simulações de Monte Carlo. Exemplos numéricos considerando dados reais e simulados são apresentados para ilustrar a metodologia desenvolvida / Abstrac: In this work, we studied some aspects of estimation and diagnostics on the global and local influence in nonlinear models under the class of scale mixtures of the skewnormal (SMSN) distribution, based on the methodology proposed by Cook (1986) e Poon & Poon (1999). Heteroscedastic nonlinear models are also discussed. This new class of models are a robust generalization of non-linear regression symmetrical models, which have as members individual distributions with heavy tails, such as skew-t, skew-slash, and skew-contaminated normal, among others. The parameter estimation will be obtained with the EM algorithm proposed by Dempster et al. (1977). Studies testing hypotheses are considered using the score statistics and the likelihood ratio test to test the homogeneity of scale parameter. Properties of test statistics are investigated through Monte Carlo simulations. Numerical examples considering real and simulated data are presented to illustrate the methodology / Mestrado / Métodos Estatísticos / Mestre em Estatística

The use of distributed systems, involving multiple components, has become a common industry practice. However, modeling the behaviour of such systems is a challenge, especially when the behavior consists of several collaborations of different parties, each involving possibly several starting (input) and ending (output) events of the involved components. Furthermore, the global behavior should be described as a composition of several sub-behaviours, in the following called collaborations, and each collaboration may be further decomposed into several sub-collaborations. We assume that the performance of the elementary sub-collaborations is known, and that the performance of the global behavior should be determined from the performance of the contained elementary collaborations and the form of the composition. A collaboration, in this thesis, is characterized by a partial order of input and output events, and the performance of the collaboration is defined by the minimum delays required for a given output event with respect to an input event. This is a generalization of the semantics of UML Activities, where all input events are assumed to occur at the same time, and all output events occur at the same time. We give a semantic definition of the dynamic behavior of composed collaborations using the composition operators for control flow from UML Activity diagrams, in terms of partial order relationships among the involved input and output events. Based on these semantics, we provide formulas for calculating the performance of composed collaborations in terms of the performance of the sub-collaborations, where each delay is characterized by (a) a fixed value, (b) a range of values, and (c) a distribution (in the case of stochastic behaviours). We also propose approximations for the case of stochastic behavior with Normal distributions, and discuss the expected errors that may be introduced due to ignoring of shared resources or possible dependencies in the case of stochastic behaviours. A tool has been developed for evaluating the performance of complex collaborations, and examples and case studies are discussed to illustrate the applicability of the performance analysis and the visual notation which we introduced for representing the partial-order relationships of the input and output events.

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The aim of this work is to present an inference and diagnostic study of an extension of the lifetime distribution family proposed by Birnbaum and Saunders (1969a,b). This extension is obtained by considering a skew-elliptical distribution instead of the normal distribution. Specifically, in this work we develop a Birnbaum-Saunders (BS) distribution type based on scale mixtures of skew-normal distributions (SMSN). The resulting family of lifetime distributions represents a robust extension of the usual BS distribution. Based on this family, we reproduce the usual properties of the BS distribution, and present an estimation method based on the EM algorithm. In addition, we present regression models associated with the BS distributions (based on scale mixtures of skew-normal), which are developed as an extension of the sinh-normal distribution (Rieck and Nedelman, 1991). For this model we consider an estimation and diagnostic study for uncensored data. / O objetivo deste trabalho é apresentar um estudo de inferência e diagnóstico em uma extensão da família de distribuições de tempos de vida proposta por Birnbaum e Saunders (1969a,b). Esta extensão é obtida ao considerar uma distribuição skew-elíptica em lugar da distribuição normal. Especificamente, neste trabalho desenvolveremos um tipo de distribuição Birnbaum-Saunders (BS) baseda nas distribuições mistura de escala skew-normal (MESN). Esta família resultante de distribuições de tempos de vida representa uma extensão robusta da distribuição BS usual. Baseado nesta família, vamos reproduzir as propriedades usuais da distribuição BS, e apresentar um método de estimação baseado no algoritmo EM. Além disso, vamos apresentar modelos de regressão associado à distribuições BS (baseada na distribuição mistura de escala skew-normal), que é desenvolvida como uma extensão da distribuição senh-normal (Rieck e Nedelman, 1991), para estes vamos considerar um estudo de estimação e diagnóstisco para dados sem censura.