Adaptive Efficient and Double-Robust Regression Based on Generalized Empirical Likelihood for Longitudinal Data

In this paper, we propose adaptive efficient and double-robust method to estimate mean and covariance simultaneously for longitudinal data in linear regression model. The proposed method is based on generalized empirical likelihood framework and weighted least squares. The efficient and robust estimation of mean and covariance for longitudinal data can be gained simultaneously via empirical likelihood method after the regression model is rewrited according to Cholesky decomposition. Efficiency of the proposed method is ensured via its close connection with empirical likelihood estimation while the double robustness is obtained by weighted least-square and downweighting the impact of leverage points. We also introduce a tuning parameter chosen according to the robustified generalized cross-validation statistics to make the proposed double-robust estimator adaptive. Theoretical results show the asymptotic normality. The results of finite-sample studies show the proposed estimator's high efficiency and comparable robustness toward both outliers and leverage points in comparison with some existing robust regression estimators. In the end, an application to a real data set is also presented for further illustration.