Semiparametric Estimation of Covariance Function for Longitudinal Data Jianqing Fan, Princeton University, USA Tao Huang, Yale University, USA Runze LI, Department of Statistics, Penn State University, USA, E-mail: [email protected]
Key words: Local linear regression, semiparametric modeling, semiparametric varying-coefficient partially linear 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 nonparametric variance function, and quasi-likelhood approach and minimal generalized variance method are proposed for estimation of parameters of correlation structure. We introduce semiparametric varying coefficient partially linear models for longitudinal data and propose an estimation procedure for their regression coefficients by using profile weighted least squares approach. Sampling properties of the proposed estimation procedures are studied and asymptotic 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 of a real data example.
References  Cai, Z., Fan, J. and Li, R. (2000). Efficient Estimation and Inferences for Varying- coefficient Models, Journal of the American Statistical Association, 95, 888-902.  Zhang, W., Lee, S.Y. and Song, X. (2002). Local Polynomial Fitting in Semivarying Coefficient Models, Jour. Multivar. Anal., 82, 166-188.