Partially functional linear quantile regression model and variable selection with censoring indicators MAR

In this paper, we study the quantile regression (QR) estimation for the partially functional linear model with the responses being right-censored and the censoring indicators being missing at random (MAR). Firstly, we construct the weighted QR estimators for both the infinite-dimensional slope function and the finite scalar parameters of the model by combining the methods of calibration, imputation and inverse probability weighting. Then, some asymptotic properties such as the convergence rate of the estimator for the slope function and the asymptotic distribution of the estimator for the finite scalar parameters are obtained respectively. Moreover, to select the scalar covariates in the model, we also give a variable selection procedure by the method of adaptive LASSO penalty and establish the oracle property of the proposed weighted penalized estimators simultaneously. Finally, some simulation studies and a real data analysis are carried out to show the performances of the proposed methods.