Abstract

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.

摘要

本文考虑线性回归模型的高效且稳健的估计器。在本文中，我们开发了一种基于广义经验似然框架和加权最小二乘法的自适应高效双鲁棒估计器。通过最小化差异统计来保证效率，通过加权最小二乘以及降低杠杆点的影响来获得双重鲁棒性。我们引入了一个调整参数，该参数通过稳健的广义交叉验证统计来自适应选择。所涉及的约束优化问题通过非线性规划方法来解决。理论结果显示渐近正态性。有限样本研究表明，与一些现有的鲁棒回归估计器相比，所提出的估计器具有相对较高的效率和相当的鲁棒性。仿真结果还表明，所提出的估计器对于异常值和杠杆点具有双重鲁棒性。还提出了在真实数据集上的应用，以进行进一步的说明和比较。