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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (3): 88-99.doi: 10.6040/j.issn.1671-9352.0.2023.226

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线性混合效应模型的复合分位数回归估计

李京1,杨宜平1,2*,赵培信1,2   

  1. 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
  • 发布日期:2025-03-10
  • 通讯作者: 杨宜平(1981— ),女,教授,博士,研究方向为非参数统计及数据分析. E-mail:yeepingyang@foxmail.com
  • 作者简介:李京(1999— ),男,硕士研究生,研究方向为数理统计. E-mail:1728630092@qq.com*通信作者:杨宜平(1981— ),女,教授,博士,研究方向为非参数统计及数据分析. E-mail:yeepingyang@foxmail.com
  • 基金资助:
    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)

Composite quantile regression estimation of linear mixed effects model

LI Jing1, YANG Yiping1,2 Symbolj@@, ZHAO Peixin1,2   

  1. 1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
    2. Chongqing Key Laboratory of Social Economic and Applied Statistics, Chongqing 400067, China
  • Published:2025-03-10

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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。

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

Abstract: 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.

Key words: linear mixed effect model, QR decomposition, composite quantile regression, fixed effect, random effect

中图分类号: 

  • O212.7
[1] CUI H J, NG K W, ZHU L X. Estimation in mixed effects model with errors in variables[J]. Journal of Multivariate Analysis, 2004, 91(1):53-73.
[2] WU Ping, ZHU Lixing. An orthogonality-based estimation of moments for linear mixed models[J]. Scandinavian Journal of Statistics,2010,37:253-263.
[3] 陈心洁,林鹏,邹国华. 线性混合效应模型的FIC选择准则[J]. 统计研究,2015,32(3):100-103. CHEN Xinjie, LIN Peng, ZOU Guohua. FIC selection criteria for linear mixed effects models[J]. Statistical Research, 2015, 32(3):100-103.
[4] 林鹏. 一般线性混合效应模型的随机效应选择研究[J]. 系统科学与数学,2015,35(6):617-626. LIN Peng. Research on random effects selection for general linear mixed effects model[J]. Journal of Systems Science and Mathematical Sciences, 2015, 35(6):617-626.
[5] 赵培信,张帆,周小双. 不完全观测数据下混合效应模型的正交投影估计[J]. 工程数学学报,2023,40(1):97-109. ZHAO Peixin, ZHANG Fan, ZHOU Xiaoshuang. Orthogonal projection estimation for mixed effects models with incomplete observations data [J]. Chinese Journal of Engineering Mathematics, 2023, 40(1):97-109.
[6] ZOU Hui, YUAN Ming. Composite quantile regression and the oracle model selection theory[J]. The Annals of Statistics, 2008, 36(3):1108-1126.
[7] 王康宁,李劭珉,林路. 基于copula函数的纵向数据复合分位数回归及变量选择[J]. 中国科学(数学),2020,50(8):1097-1116. WANG Kangning, LI Shaomin, LIN Lu. Composite quantile regression and variable selection of longitudinal data based on copula function [J]. Science China Mathematics, 2020, 50(8):1097-1116.
[8] 刘艳霞,芮荣祥,田茂再. 部分线性变系数模型的新复合分位数回归估计[J]. 应用数学学报,2021,44(2):159-174. LIU Yanxia, RUI Rongxiang, TIAN Maozai. New composite quantile regression estimation for partial linear variable coefficient models [J]. Acta Mathematicae Applicatae Sinica, 2021, 44(2):159-174.
[9] 张永霞,田茂再. 基于贝叶斯的部分线性单指标复合分位回归的研究及其应用[J]. 系统科学与数学,2021,41(5):1381-1399. ZHANG Yongxia, TIAN Maozai. Research and application of partial linear single index composite quantile regression based on Bayes [J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(5):1381-1399.
[10] 张立文,程东坡,薛文骏,等. 复合分位数下门限自回归模型的变点估计[J]. 中国科学(数学),2022,52(1):63-84. ZHANG Liwen, CHENG Dongpo, XUE Wenjun, et al. Change point estimation of autoregressive model with lower threshold of composite quantile [J]. Science China Mathematics, 2022, 52(1): 63-84.
[11] JIANG Rong, SUN Mengxian. Single-index composite quantile regression for ultra-high-dimensional date[J]. TEST, 2022, 31(2):443-460.
[12] GUO Chaohui, LYU Jing, WU Jibo. Composite quantile regression for ultra-high dimensional semiparametric modle averaging[J]. Computational Statistics & Data Analysis, 2021, 160:107231.
[13] KNIGHT K. Limiting distributions for l1 regression estimators under general conditions[J]. The Annals of Statistics, 1998, 26(2):755-770.
[14] MUNNELL A. Why has productivity growth declined productivity and public investment[J]. New England Economic Review, 1990, 1(2):3-22.
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