Wavelet estimation in nonparametric linear mixed-effects errors in variables model

Abstract

Nonparametric linear mixed effects models are preferred due to overcome the restrictions of linear models which need to satisfy distributional assumptions. In these models, smoothing approaches are needed to handle nonparametric part and chosen according to the type of data. When there is a measurement error in the nonparametric part, these smoothing techniques become more complicated. In this paper, we propose wavelet approach to smooth nonparametric function under known measurement error in nonparametric linear mixed effects model and then, we predict random effects pa rameter. Fu rthermore, a si mulation study is done to demonstrate the theoretical findings by comparing with the case ignoring measurement error. The performances are much better for the proposed model than the no measurement error case.