纵向数据下基于广义经验似然的有效自适应双稳健回归  

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

作　　者：向亚云 樊亚莉[1] XIANG Yayun;FAN Yali(College of Science,University of Shanghai for Science and Technology,Shanghai,200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《应用概率统计》2022年第5期723-744,共22页Chinese Journal of Applied Probability and Statistics

摘　　要：本文对纵向数据下的线性回归模型提出了一种同时估计协方差矩阵以及均值的有效自适应双稳健回归方法.该方法以广义经验似然为基础并结合加权最小二乘思想,首先用Cholesky分解将纵向数据的线性模型重参数化,再用广义经验似然估计方法,同时实现对协方差矩阵以及均值的有效稳健估计.有效性通过所提方法与广义经验似然方法的紧密联系获得,而加权最小二乘以及对杠杆点的降权使得该估计具有双重稳健性.本文在计算过程中还引入了一个调节参数,该参数的选定是依据稳健广义交叉验证统计量,这使得本文的双稳健估计对数据具有自适应性.理论结果展示了本文估计参数的渐近正态性.有限样本研究的结果显示,与一些现有的经典稳健估计方法相比,所提的方法在保持较高有效性的同时还具备相当好的稳健性.本文还做了一个真实数据分析来做进一步的比较.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.

关 键 词：纵向数据 有效估计 双重稳健性 CHOLESKY分解 广义经验似然 加权最小二乘 

分 类 号：O212.1[理学—概率论与数理统计]