删失指标随机缺失下部分线性模型的稳健估计及变量选择  

Robust estimators and variable selection for partially linear models with censoring indicators missing at random

作　　者：饶珍敏 王江峰[1,2] 陈定凯 王磊 RAO Zhen-min;WANG Jiang-feng;CHEN Ding-kai;WANG lei(School of Statis.Math.,Zhejiang Gongshang Univ.,Hangzhou 310018,China;Center of Statistical Data Engineering,Technology&Application,Zhejiang Gongshang Univ.,Hangzhou 310018,China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018 [2]浙江工商大学统计数据工程技术与应用协同创新中心,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2023年第1期1-17,共17页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家社会科学基金(20BTJ049);浙江工商大学研究生科研创新基金。

摘　　要：在删失指标随机缺失数据下,研究部分线性模型的复合分位数回归估计.基于校准和插值两种方法,根据三步法构建线性参数和非参数函数的CQR估计量.与此同时,利用自适应LASSO惩罚方法,对线性参数进行变量选择.在适当的假设下,证明了估计量的渐近正态性,受惩罚的估计量被证明具有oracle性质.最后通过模拟研究评估参数估计量和非参数函数估计量的性能.This paper focuses on the composite quantile regression of partially linear models when the data are right censored and the censoring indicators are missing at random. Based on the calibration and the imputation methods, a three-stage approach is proposed to construct the estimators of the linear part and the nonparametric function for this model. Meanwhile, this paper discusses the variable selection of the covariates in the linear part by adopting the adaptive LASSO penalty. Under appropriate assumptions, the asymptotic normality of the proposed estimators is established, and the penalized estimators are proven to have the oracle property. The simulation study is conducted to evaluate the performance of the proposed estimators.

关 键 词：删失指标 随机缺失 复合分位数回归 部分线性回归模型 变量选择 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]