Efficient semiparametric estimation via Cholesky decomposition for longitudinal data

Semiparametric methods for longitudinal data with dependence within subjects have recently received considerable attention. Existing approaches that focus on modeling the mean structure require a correct specification of the covariance structure as misspecified covariance structures may lead to inefficient or biased mean parameter estimates. Besides, computation and estimation problems arise when the repeated measurements are taken at irregular and possibly subject-specific time points, the dimension of the covariance matrix is large, and the positive definiteness of the covariance matrix is required. In this article, we propose a profile kernel approach based on semiparametric partially linear regression models for the mean and model covariance structures simultaneously, motivated by the modified Cholesky decomposition. We also study the large-sample properties of the parameter estimates. The proposed method is evaluated through simulation and applied to a real dataset. Both theoretical and empirical results indicate that properly taking into account the within-subject correlation among the responses using our method can substantially improve efficiency.