Statistical Modelling 6 (2006), 59–76

Assessment of variance components in elliptical linear mixed models

Carine Savalli
Instituto de Mathemática e Estatística,
Universidade de São Paulo

Gilberto A. Paula
Instituto de Mathemática e Estatística,
Universidade de São Paulo,
USP-Caixa Postal 66281 (Ag. Cidade de São Paulo),
05311–970 São Paulo, SP
Brazil
eMail: giapaula@ime.usp.br

Francisco J.A. Cysneiros
Universidade Federal de Pernambuco
Brazil

Abstract:

The aim of this article is to discuss the problem of testing variance components in elliptical linear mixed models. The elliptical class includes all symmetrical continuous distributions, such as normal, Student-t, Pearson VII, power exponential, logistic I, logistic II, and so on. An approach for elliptical linear mixed models is proposed. The estimation procedure for the fixed parameters, variance components and random effects is also presented and a score-type test for one-sided alternatives to assess the variance components is investigated. Finally, two illustrative examples are given in which normal linear mixed models are compared with elliptical linear mixed models with heavy-tailed error distributions.

Keywords:

Elliptical distributions; hypothesis testing; one-sided alternatives; robust models; score tests; variance components
 

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