HIGH DIMENSIONAL CENSORED QUANTILE REGRESSION.

Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. We propose a two-step penalization procedure, which accommodates stochastic integral based estimating equations and address the challenges due to the recursive nature of the procedure. We establish the uniform convergence rates for the proposed estimators, and investigate the properties on weak convergence and variable selection. We conduct numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposals.