Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge for large-scale data with many covariates. In this paper, we focus on a smoothed martingale-based sequential estimating equations approach, to which scalable gradient-based algorithms can be applied. Theoretically, we provide a unified analysis of the smoothed sequential estimator and its penalized counterpart in increasing dimensions. When the covariate dimension grows with the sample size at a sublinear rate, we establish the uniform convergence rate (over a range of quantile indexes) and provide a rigorous justification for the validity of a multiplier bootstrap procedure for inference. In high-dimensional sparse settings, our results considerably improve the existing work on CQR by relaxing an exponential term of sparsity. We also demonstrate the advantage of the smoothed CQR over existing methods with both simulated experiments and data applications.
X. He was supported by NSF Grants DMS-1914496 and DMS-1951980. K. M. Tan was supported by NSF Grants DMS-1949730, DMS-2113356 and NIH Grant RF1-MH122833. W.-X. Zhou acknowledges the support of the NSF Grant DMS-2113409.
The authors acknowledge two anonymous referees and an Associate Editor for their constructive comments that improved the quality and presentation of this paper.
"Scalable estimation and inference for censored quantile regression process." Ann. Statist. 50 (5) 2899 - 2924, October 2022. https://doi.org/10.1214/22-AOS2214