Lack-of-fit tests in linear mixed models with application to wavelet tests

Gerda Claeskens, Huijuan Ding and Maarten Jansen

Journal of Nonparametric Statistics, 2011, vol. 23, issue 4, 853-865

Abstract: We obtain the asymptotic distribution of score and restricted likelihood ratio statistics for testing whether variance components are equal to zero in linear mixed models with a fixed and finite number of random effects. The main new innovation of this paper is in deriving the components of the distribution, which are not chi-squared. The proposed test statistics are used for lack-of-fit testing using wavelets, where the finest scale wavelet coefficients are allowed to have a different variance than the other wavelet coefficients in the mixed effect wavelet model. We study the power of a wavelet-based test for a hypothesised parametric model within a mixed model framework in a simulation study.

Date: 2011
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DOI: 10.1080/10485252.2011.598935

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