Nonlinear models based on scale mixtures skew-normal distributions

Author(s)

Aldo William Medina Garay

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2010-08-07

Examining board members

Víctor Hugo Lachos Dávila; Mariana Rodrigues Motta; Márcia D'Elia Branco

• Advisor: Filidor Edilfonso Vilca Labra; Víctor Hugo Lachos Dávila

Abstract

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 (AU)

• FAPESP's process: 08/02159-9 - Hierarchical models with scale mixtures of skew-normal distributions
• Grantee: Aldo William Medina Garay
• Support Opportunities: Scholarships in Brazil - Master