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

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  • Gerda Claeskens
  • Huijuan Ding
  • Maarten Jansen

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.

Suggested Citation

  • Gerda Claeskens & Huijuan Ding & Maarten Jansen, 2011. "Lack-of-fit tests in linear mixed models with application to wavelet tests," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 853-865.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:853-865
    DOI: 10.1080/10485252.2011.598935
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