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

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.