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Estimation methods in heavy-tailed nonlinear mixed effects models

Gomes, José Clelto Barros

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Estatística Interinstitucional do ICMC e UFSCarr 2019-12-05

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  • Título:
    Estimation methods in heavy-tailed nonlinear mixed effects models
  • Autor: Gomes, José Clelto Barros
  • Orientador: Novelli, Cibele Maria Russo
  • Assuntos: Métodos De Estimação; Dados Correlacionados; Máxima Verossimilhança; Máxima Verossimilhança Restrita; Modelos Não-Lineares; Modelos Mistos; Nonlinear Models; Mixed-Effects Models; Correlated Data; Maximum Likelihood; Estimation Methods; Restricted Maximum Likelihood
  • Notas: Tese (Doutorado)
  • Descrição: Parameter estimation in nonlinear mixed-effects models is often challenging. In this thesis, a comparison of estimation methods for these models is proposed under a frequentist approach. In the first study, a comparison of maximum likelihood estimates under an exact method via Monte Carlo expectation-maximization (MCEM) and an approximate method based on a Taylor expansion, frequently used in the literature, is provided. In a second study, a restricted maximum likelihood estimation method is proposed, aiming to decrease the bias for the variance components estimates, based on the integration of the likelihood function on the fixed-effects, also in an exact likelihood context. These estimates are compared to the maximum likelihood ones. For the latter comparison, stochastic approximation of expectation-maximization (SAEM) algorithms are considered. The random effects and errors are assumed to follow multivariate symmetric distributions, namely the scale mixture of normal distributions, which include the normal, t and slash distributions. Finally, a general nonlinear mixed-effects model is proposed, where no linear relation is assumed in the random effects structure. In all the proposals, real data sets and simulation studies are used to illustrate the estimates properties.
  • DOI: 10.11606/T.104.2020.tde-20032020-171207
  • Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Estatística Interinstitucional do ICMC e UFSCarr
  • Data de criação/publicação: 2019-12-05
  • Formato: Adobe PDF
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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