Semiparametric Estimation of Covariance Function for Longitudinal Data

models Mathematical Subject Classification: 62G08, 62G20 Abstract: It is challenging in estimating covariance function of longitudinal data collected at irregular time points. In this paper, we propose a class of semiparametric models for covariance function by imposing parametric correlation structure and allowing nonparametric variance function. Kernel estimator is developed for estimation of nonpara-metric variance function, and quasi-likelhood approach and minimal generalized variance method are proposed for estimation of parameters of correlation structure. We introduce semiparametric varying coecient partially linear models for longitudinal data and propose an estimation procedure for their regression coecients by using prole weighted least squares approach. Sampling properties of the proposed estimation procedures are studied and asymp-totic normality of the resulting estimator are established. Finite sample performance of the proposed procedures are assessed by Monte Carlo simulation studies. Furthermore, the proposed methodology is illustrated by an analysis o