Statistical Modelling 12 (2012), 165–193

Influence diagnostics for elliptical semiparametric mixed models

Germán Ibacache-Pulgar
Universidade de São Paulo
Brazil
eMail: germanp@ime.usp.br

Gilberto A Paula
Instituto de Matemática e Estatística, USP
Rua do Matão 1010, Cidade Universitária
05508-090 São Paulo SP
Brazil
eMail: giapaula@ime.usp.br

Abstract:

In this paper we extend semiparametric mixed linear models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. Penalized likelihood equations are applied to derive the maximum penalized likelihood estimates (MPLEs) which appear to be robust against outlying observations in the sense of the Mahalanobis distance. A reweighed iterative process based on the back-fitting method is proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to study the sensitivity of the MPLEs. Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering some appropriate elliptical errors. The local influence approach is used to compare the sensitivity of the model estimates.

Keywords:

elliptical distributions; maximum penalized likelihood estimates; nonparametric models; robust estimates; sensitivity analysis

Downloads:

Matlab Code in zipped archive; R package developed after publication of the paper.
back