Statistical diagnostics for nonlinear regression models based on scale mixtures of skew-normal distributions

Author(s)

Garay, Aldo M. ^[1] ; Lachos, Victor H. ^[2] ; Labra, Filidor V. ^[2] ; Ortega, Edwin M. M. ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

^[2] Univ Estatual Campinas, Dept Estat, Sao Paulo - Brazil

^[3] Univ Sao Paulo, Dept Ciencias Exatas, Sao Paulo - Brazil

• Document type: Journal article
• Source: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION; v. 84, n. 8, p. 1761-1778, AUG 3 2014.
• Web of Science Citations: 3

Abstract

The purpose of this paper is to develop diagnostics analysis for nonlinear regression models (NLMs) under scale mixtures of skew-normal (SMSN) distributions introduced by Garay et al. {[}Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115-124]. This novel class of models provides a useful generalization of the symmetrical NLM {[}Vanegas LH, Cysneiros FJA. Assessment of diagnostic procedures in symmetrical nonlinear regression models. Comput. Statist. Data Anal. 2010;54:1002-1016] since the random terms distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as the skew-t, skew-slash, skew-contaminated normal distributions, among others. Motivated by the results given in Garay et al. {[}Nonlinear regression models based on SMSN distributions. J. Korean Statist. Soc. 2011;40:115-124], we presented a score test for testing the homogeneity of the scale parameter and its properties are investigated through Monte Carlo simulations studies. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. The newly developed procedures are illustrated considering a real data set. (AU)

• FAPESP's process: 11/17400-6 - Applications of the scale mixture of Skew-Normal distributions in linear mixed effects models
• Grantee: Víctor Hugo Lachos Dávila
• Support Opportunities: Regular Research Grants