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

摘要

We consider a linear mixed-effects model where Y_(k,j) = α_k+ β_k~t_k + ε_(kj) 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 tj, we show that a completely data-driven strategy can be implemented without any knowledge on the noise density. Intensive simulation experiments illustrate the method.