Open Access
August 2020 Double-slicing assisted sufficient dimension reduction for high-dimensional censored data
Shanshan Ding, Wei Qian, Lan Wang
Ann. Statist. 48(4): 2132-2154 (August 2020). DOI: 10.1214/19-AOS1880


This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time $T$ depends on a high-dimensional covariate vector $\mathbf{X}$ through low-dimensional linear combinations of covariates $\Gamma ^{T}\mathbf{X}$. The censoring time is allowed to be conditionally independent of the survival time given the covariates. This general framework includes many popular parametric and semiparametric survival regression models as special cases. The proposed algorithm produces a number of practically useful outputs with theoretical guarantees, including a consistent estimate of the sufficient dimension reduction subspace of $T\mid \mathbf{X}$, a uniformly consistent Kaplan–Meier-type estimator of the conditional distribution function of $T$ and a consistent estimator of the conditional quantile survival time. Our asymptotic results significantly extend the classical theory of sufficient dimension reduction for censored data (particularly that of Li, Wang and Chen in Ann. Statist. 27 (1999) 1–23) and the celebrated nonparametric Kaplan–Meier estimator to the setting where the number of covariates $p$ diverges exponentially fast with the sample size $n$. We demonstrate the promising performance of the proposed new estimators through simulations and a real data example.


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Shanshan Ding. Wei Qian. Lan Wang. "Double-slicing assisted sufficient dimension reduction for high-dimensional censored data." Ann. Statist. 48 (4) 2132 - 2154, August 2020.


Received: 1 February 2018; Revised: 1 June 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134789
Digital Object Identifier: 10.1214/19-AOS1880

Primary: 62H20 , 62J07
Secondary: 62N02

Keywords: Censored data , central subspace , nonparametric estimation , sufficient dimension reduction , ultrahigh dimension , Variable selection

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 4 • August 2020
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