Double Smoothing Estimation For Two Semi-Parametric Regression Models With Longitudinal Data

In a longitudinal data study, there exists essential difference with that for independent data because of the special structure. Many outstanding research results have been proposed based on partial linear model and varying coefficient model. We used the double smoothing estima-tion method instead of the normal local linear estimation under longitudinal data to discuss the estimation problem of partial linear model and varying coefficient model. A comparison of the two estimators indicated that our new method can reduce the asymptotic bias from the order of Op(h2) to the order of Op(h4) without changing the order of asymptotic variance.In this paper we firstly introduced the semi-parametric regression model, the definition of longitudinal data and the research status, and focused on the longitudinal data of partial lin-ear model and varying coefficient model, besides the double smoothing local linear estimation. Then for the partial linear model with longitudinal data, we made use of the former estimation of parametric and nonparametric components, and proposed the new double smoothing local linear estimator. We also compared the asymptotic bias,asymptotic variance and asymptotic normality of the new estimator with previous estimators. Under the longitudinal data with varying coeffi-cient model, we first gave its local linear estimation method, and then proposed the new double smoothing local linear estimator, which was similar to that of partial linear model. Simulation studies under the longitudinal data of partial linear model and varying coefficient model were conducted respectively. And we also applied the double smoothing local linear estimation to the study of CD4 cell data case.