Local estimation for longitudinal semiparametric varying-coefficient partially linear model

In this paper, estimation for the semiparametric varying coefficient partially linear model with longitudinal data is investigated. We propose an intuitive procedure to estimate the regression function and the covariance structure simultaneously based on the modified Cholesky decomposition and profile least square technique. The asymptotic normality of the resulting estimators is further derived. Moreover, we develop a variable selection procedure to select significant parameter components for the model within the framework of profile least square estimate. A simulation study is conducted to illustrate the finite-sample performance of the estimation and variable selection procedures. Finally, the proposed method is applied to analyze a set of chronic kidney disease (CKD) progression data in a study of the relationship between glomerular filtration rate (GFR) and the risk factors among CKD patients.