Banca de DEFESA: ROMMY CAMASCA OLIVARI

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : ROMMY CAMASCA OLIVARI
DATE: 14/02/2023
TIME: 14:00
LOCAL: Departamento de Estatística
TITLE:

Nonlinear mixed effects models for censored data considering elliptical autoregressive errors

KEY WORDS:

Autoregressive AR(p) errors, Censored data, Elliptical distribution, EM algorithm, Martingale residuals, Nonlinear mixed-effects model

PAGES: 60
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUMMARY:

Mixed effects models are frequently used tools for studying longitudinal data. However, due to the possible complexity of this type of data, it is attractive to develop extensions of these models with more flexible assumptions aimed at improving the fit of the data. In this context, we propose a more flexible extension of mixed effects models with censored responses and autoregressive normal errors of order $p$. For this, we initially assign the elliptical distribution class to the random components of the model. This family of distributions will allow us to work with datasets with lighter or heavier tails than normal, allowing a less sensitive fit to the presence of atypical observations. Thus, an EM-type algorithm was developed to obtain the maximum likelihood estimates and the standard errors of these estimates using the empirical information matrix. On the other hand, in the last few years, there has been a growing interest in statistical methods for analyzing longitudinal data with spatial effects. In this context, we propose a second extension of the initially proposed model, including spatial dependence in the distribution of the random effect. To assess the goodness of fit and assumptions of the proposed models, martingale residuals and diagnostic measures were used based on the global and local influence approach. We present simulation studies under different scenarios to evaluate the asymptotic properties of the estimators and the performance of this class of models in the presence of outliers. Finally, practical examples with real data were analyzed.

COMMITTEE MEMBERS:
Presidente - 2259583 - ALDO WILLIAM MEDINA GARAY
Interna - 2259568 - FRANCYELLE DE LIMA MEDINA
Interno - 1142348 - ROBERTO FERREIRA MANGHI
Externo à Instituição - CELSO RÔMULO BARBOSA CABRAL - UFAM
Externo à Instituição - JUVENCIO SANTOS NOBRE - UFC