Joint semiparametric mean-covariance model in longitudinal study

• Published in: Science China. Mathematics Vol. 54; no. 1; pp. 145 - 164
• Main Authors: Mao, Jie, Zhu, ZhongYi
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Science China Press 01.01.2011
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; local linear regression; semiparametric varying-coefficient partially linear model; 62G08; 62G20; generalized estimating equation; 62F12; kernel estimation; modified Cholesky decomposition
• ISSN: 1674-7283; 1869-1862
• DOI: 10.1007/s11425-010-4078-4

Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.