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

This article considers the efficient and robust estimators for linear regression models. In this article, we develop an adaptive efficient and double-robust estimator based on generalized empirical likelihood framework and weighted least squares. Efficiency is ensured through minimizing the discrepancy statistics and the double robustness is obtained via weighted least-square as well as downweighting the impact of leverage points. We introduce a tuning parameter which is chosen adaptively through the robustified generalized cross-validation statistics. The constrained optimization problem concerned is solved through nonlinear programming approaches. Theoretical results show the asymptotic normality. It is presented in the finite-sample studies that the proposed estimator possesses relatively high efficiency and comparable robustness in comparison with some existing robust regression estimators. Simulation results also indicate that the proposed estimator is double-robust toward both outliers and leverage points. An application to a real data set is also presented for further illustration and comparison.