线性混合效应模型的复合分位数回归估计  

Composite quantile regression estimation of linear mixed effects model

作　　者：李京 杨宜平[1,2] 赵培信 LI Jing;YANG Yiping;ZHAO Peixin(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economic and Applied Statistics,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《山东大学学报(理学版)》2025年第3期88-99,共12页Journal of Shandong University(Natural Science)

基　　金：国家社会科学基金资助项目(18BTJ035);重庆市自然科学基金资助项目(cstc2021jcyj-msxmX0079,cstc2020jcyj-msxmX0006);重庆市教委人文社科一般项目(21SIGH118);重庆市社科规划委托项目(2019WT58);第五批重庆市高等学校优秀人才支持计划(68021900601)。

摘　　要：考虑线性混合效应模型的稳健估计问题,通过结合矩阵的QR分解技术和复合分位数回归方法,提出一种基于正交投影的复合分位数回归估计方法。先通过QR分解技术消除随机效应,再构造固定效应的复合分位数回归目标函数,从而获得固定效应的估计。在一些正则条件下,证明所提出估计的渐近正态性。所提出的估计方法无需对模型误差和随机效应的分布作任何限制性的假定,并且固定效应的估计不受随机效应的影响。与正交矩估计方法的模拟研究比较表明,本文提出的方法具有稳健性,并将其应用于实际数据分析。Considering the robust estimation problem of linear mixed effect model,a composite quantile regression estimation method based on orthogonal projection is proposed by combining the QR decomposition technique of matrix and the composite quantile regression method.The random effects are eliminated by QR decomposition technique,and then the fixed effects are estimated by constructing the composite quantile regression objective function.Under some regular conditions,the asymptotic normality of the proposed estimates is proved.The proposed estimation method does not need to make any restrictive assumptions about the distribution of model errors and random effects,and the estimates of fixed effects are not affected by random effects.Further,the simulation study compares the proposed method with the orthogonality-based estimation of moment method,which shows that the proposed method is robust and applied to the actual data analysis.

关 键 词：线性混合效应模型 QR分解 复合分位数回归 固定效应 随机效应 

分 类 号：O212.7[理学—概率论与数理统计]