Nonparametric estimations for the cumulative distribution functions of random effects in a linear mixed-effects model

This article is devoted to the nonparametric estimation problem of the cumulative distribution functions of random effects in a linear mixed-effects model. Random noises in the model are assumed to have a symmetric distribution. Applying deconvolution methods, we build appropriate estimators for the target functions and then study some of their asymptotic properties with respect to the mean squared errors. Some numerical experiments are also conducted to illustrate the convergence of the proposed estimators.