Semiparametric Mean-Covariance\nRegression Analysis for Longitudinal Data

Abstract

E±cient estimation of the regression coe±cients in longitudinal data anal-\nysis requires a correct speci¯cation of the covariance structure. Existing ap-\nproaches usually focus on modeling the mean with speci¯cation of certain co-\nvariance structures, which may lead to ine±cient or biased estimators of pa-\nrameters in the mean if misspeci¯cation occurs. In this paper, we propose a\ndata-driven approach based on semiparametric regression models for the mean\nand the covariance simultaneously, motivated by the modi¯ed Cholesky de-\ncomposition. A regression spline based approach using generalized estimating equations is developed to estimate the parameters in the mean and the covari-\nance. The resulting estimators for the regression coe±cients in both the mean\nand the covariance are shown to be consistent and asymptotically normally dis-\ntributed. In addition, the nonparametric functions in these two structures are\nestimated at their optimal rate of convergence. Simulation studies and a real\ndata analysis show that the proposed approach yields highly e±cient estimators\nfor the parameters in the mean, and provides parsimonious estimation for the\ncovariance structure.