Efficient Robust Estimation of Mean and Covariance for Longitudinal Data

In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.