Quantile regression and variable selection for partially linear single-index models with missing censoring indicators

Abstract

Partially linear single-index models have been studied extensively under censorship setting, but typically all of the censoring indicators are assumed to be observed. This paper focuses on the quantile regression (QR) estimation for the partially linear single-index models where the data are right censored and the censoring indicators are missing at random. We propose weighted QR estimators of unknown parameters and link function based on the regression calibration, imputation and inverse probability weighting approaches. The asymptotic properties of the proposed weighted QR estimators for unknown parameters and the link function are established. Moreover, to select the important predictors, a variable selection procedure is introduced by applying adaptive LASSO penalized and the oracle property of the proposed weighted penalized estimators is obtained simultaneously. The finite sample performance of the proposed estimation methods and variable selection procedure are evaluated via simulation study. We also illustrate the proposed methods by using a dataset from a breast cancer clinical trial.