Nonparametric estimation of random-effects densities in linear mixed-effects model

Fabienne Comte and Adeline Samson

Journal of Nonparametric Statistics, 2012, vol. 24, issue 4, 951-975

Abstract: We consider a linear mixed-effects model where Y k, j =α k +β k t j +ϵ k, j is the observed value for individual k at time t j , k =1, ..., N, j =0, 1, ..., J . The random effects (α k , β k ) k are independent and identically distributed random variables with unknown densities f α and f β and are independent of noise. We develop nonparametric estimators of these two densities, which involve a cut-off parameter. We study their mean integrated squared risk and propose cut-off selection strategies, depending on the noise distribution assumptions. Finally, in the particular case of fixed interval between times t j , we show that a completely data-driven strategy can be implemented without any knowledge on the noise density. Intensive simulation experiments illustrate the method.

Date: 2012
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DOI: 10.1080/10485252.2012.731056

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