混合随机缺失数据下测量误差模型的复合分位数回归  

Composite Quantile Regression for Measurement Error Models with Mixed Random Missing Data

作　　者：徐红霞 林鑫达 范国良 XU Hongxia;LIN Xinda;FAN Guoliang(School of Science,Shanghai Maritime University,Shanghai 201306;School of Economics&Management,Shanghai Maritime University,Shanghai 201306)

机构地区：[1]上海海事大学理学院,上海201306 [2]上海海事大学经济管理学院,上海201306

出　　处：《系统科学与数学》2024年第8期2476-2495,共20页Journal of Systems Science and Mathematical Sciences

基　　金：国家社科基金(21BTJ038,22BTJ018)资助课题。

摘　　要：文章研究了响应变量和多维协变量混合随机缺失情况下的线性测量误差模型的复合分位数回归和变量选择问题.为提高估计效率,文章基于逆概率加权和测量误差修正因子给出回归系数的复合分位数回归估计量.该方法不仅可以消除测量误差对估计结果的影响,而且能够有效地处理混合随机缺失数据.同时获得了所提估计量的渐近正态性.进一步,文章基于自适应LASSO方法,提出混合随机缺失数据下测量误差模型的变量选择方法,并证明了惩罚估计量具有oracle性质.蒙特卡罗模拟实验和实际数据分析给出了文章所提方法在有限样本下的表现.In this paper,we study composite quantile regression(CQR)and variable selection of linear errors-in-variables models where the response and multi-dimensional covariates are mixed random missing.In order to improve the estimation efficiency,we propose the CQR estimator of regression coefficients based on inverse probability weighting and measurement error correction factor.The proposed CQR estimator can not only eliminate the influence of measurement errors on estimation results,but also deal with mixed random missing data effectively.At the same time,the asymptotic normality of the proposed estimator is obtained.Furthermore,a variable selection method based on the adaptive LASSO penalty is investigated for the measurement error models with mixed random missing data.The oracle property of the proposed penalized estimator is also established.Meanwhile,Monte Carlo simulation studies and a real data analysis are conducted to demonstrate the finite sample performance of the proposed methods.

关 键 词：复合分位数回归 测量误差 混合随机缺失 变量选择 渐近正态 

分 类 号：O212.1[理学—概率论与数理统计]