Analysis of longitudinal data with semiparametric estimation of covariance function

Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data. Both involve estimation of the covariance function. Yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed. A kernel estimator for estimating the nonparametric variance function is developed. Two methods for estimating parameters in the correlation structure - a quasi-likelihood approach and a minimum generalized variance method - are proposed. A semiparametric varying coefficient partially linear model for longitudinal data is introduced, and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed. Sampling properties of the proposed estimation procedures are studied, and asymptotic normality of the resulting estimators is established. Finite-sample performance of the proposed procedures is assessed by Monte Carlo simulation studies. The proposed methodology is illustrated with an analysis of a real data example.