The Annals of Statistics

High dimensional censored quantile regression

Qi Zheng, Limin Peng, and Xuming He

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Abstract

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.

Article information

Source
Ann. Statist., Volume 46, Number 1 (2018), 308-343.

Dates
Received: May 2016
Revised: January 2017
First available in Project Euclid: 22 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.aos/1519268432

Digital Object Identifier
doi:10.1214/17-AOS1551

Mathematical Reviews number (MathSciNet)
MR3766954

Zentralblatt MATH identifier
06865113

Subjects
Primary: 62J07: Ridge regression; shrinkage estimators
Secondary: 62H12: Estimation

Keywords
High dimensional survival data varying covariate effects censored quantile regression

Citation

Zheng, Qi; Peng, Limin; He, Xuming. High dimensional censored quantile regression. Ann. Statist. 46 (2018), no. 1, 308--343. doi:10.1214/17-AOS1551. https://projecteuclid.org/euclid.aos/1519268432


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Supplemental materials

  • Supplement to “High dimensional censored quantile regression”. Additional simulation results, remarks, and proofs of technical lemmas.