Kernel estimator and predictor of partially linear mixed-effect errors-in-variables model

This paper considers the partially linear mixed-effect model relating a response Y to predictors (X, Z, T) with mean function X-T beta + Z(T)b + g(T) which is a combination of the linear mixed-effect model and the nonparametric smooth function. The proposed model contains an additive measurement error in X. Taavoni and Arashi (Kernel estimation in semiparametric mixed-effect longitudinal modelling. Statist Papers. 2019. Available from: https://doi.org/10.1007/s00362019-01125-8.) approximated the nonparametric function by the profile kernel method, and made use of the weighted least squares to estimate the regression coefficients when measurement error was ignored. We derive a simple modification of their estimators by correction for attenuation stems from measurement error and demonstrate that the linear parts estimator is asymptotically normal.