Joint estimation of mean-covariance model for longitudinal data with basis function approximations

When the selected parametric model for the covariance structure is far from the true one, the corresponding covariance estimator could have considerable bias. To balance the variability and bias of the covariance estimator, we employ a nonparametric method. In addition, as different mean structures may lead to different estimators of the covariance matrix, we choose a semiparametric model for the mean so as to provide a stable estimate of the covariance matrix. Based on the modified Cholesky decomposition of the covariance matrix, we construct the joint mean-covariance model by modeling the smooth functions using the spline method and estimate the associated parameters using the maximum likelihood approach. A simulation study and a real data analysis are conducted to illustrate the proposed approach and demonstrate the flexibility of the suggested model.