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Doctoral Thesis
DOI
10.11606/T.45.2019.tde-11032019-160302
Document
Author
Full name
Natalia Andrea Milla Pérez
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Paula, Gilberto Alvarenga (President)
Ferrari, Silvia Lopes de Paula
Labra, Filidor Edilfonso Vilca
Novelli, Cibele Maria Russo
Rojas, Manuel Jesus Galea
Title in Portuguese
Métodos de estimação baseados na função de verossimilhança para modelos lineares elípticos
Keywords in Portuguese
Máxima verossimilhança perfilada modificada
Máxima verossimilhança restrita
Métodos robustos
Modelos exponencial potência
Modelos lineares elípticos
Modelos mistos
Modelos t-Student
Abstract in Portuguese
O objetivo desta tese é estudar métodos de estimação baseados na função de verossimilhança em modelos mistos lineares elípticos. Derivamos inicialmente os métodos de máxima verossimilhança, máxima verossimilhança restrita e de máxima verossimilhança perfilada modificada para o modelo linear normal. Estendemos os métodos para os modelos lineares elípticos e encontramos diferenças entre as equações resultantes de cada método. A principal motivação deste trabalho é que o método de máxima verossimilhança restrita tem sido aplicado para obter estimadores menos viesados para os componentes de variância-covariância, em contraste com os estimadores de máxima verossimilhança. O método tem sido muito utilizado em modelos com estruturas de variância-covariância como é o caso dos modelos mistos lineares. Assim, procuramos estender o método para os modelos mistos lineares elípticos bem como comparar com outros procedimentos de estimação, máxima verossimilhança e máxima verossimilhança perfilada modificada. Estudamos em particular os modelos mistos lineares com erros t-Student e exponencial potência.
Title in English
Estimation methods based on the likelihood function in Elliptical Linear Models
Keywords in English
Linear elliptical models
Mixed models
Modified profile maximum likelihood
Power exponencial models
Restricted maximum likelihood
Robust methods
Student-t models
Abstract in English
The aim of this thesis is to study estimation methods based on the likelihood functions in elliptical linear mixed models. First, we review the modified profile maximum likelihood and the restricted maximum likelihood methods as well as the traditional maximum likelihood method in normal linear models. Then, we extend the methodologies for elliptical linear models and we compare the estimating equations derived for each method. The main motivation of the work is that the restricted maximum likelihood method has been largely applied in normal linear mixed models in order to reduce the bias of the maximum likelihood variance-component estimators. So, we intend to investigate the possible extension for elliptical linear mixed models as well as to compare with the modified profile maximum likelihood and the maximum likelihood methods. Particular studies for Student-t and power exponential linear mixed models are presented.
 
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TeseNMPerez.pdf (8.29 Mbytes)
Publishing Date
2019-04-02
 
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