Abstract: Modeling the mean and covariance simultaneously has recently received considerable attention when efficiently analyzing the longitudinal data. An unconstrained and statistically interpretable reparameterization of covariance matrix itself was presented by utilizing a novel Cholesky factor. The entries in such decomposition have moving average and log innovation interpretation and can thus be modeled as functions of covariates. With this decomposition and the consideration of model flexibility, new semiparametric models for jointly modeling the mean and covariance itself were proposed, rather than its inverse as commonly studied in literature. A spline based approach using generalized estimating equations was developed to estimate the parameters in the mean and the covariance. It was shown that the estimators for the parametric parts in both the mean and covariance are consistent and asymptotically normally distributed, and the nonparametric parts could be estimated at an optimal rate of convergence. Simulation studies and real data analysis illustrate that the proposed approach could yield highly reliable estimation of the mean and covariance matrix.

Key words: longitudinal data, semiparametric model, generalized estimating equation, modified Cholesky decomposition, moving average, B-spline