Statistical Inference for High-Dimensional Convoluted Rank Regression
成果类型：
Article; Early Access
署名作者：
Cai, Leheng; Guo, Xu; Lian, Heng; Zhu, Liping
署名单位：
Tsinghua University; Beijing Normal University; City University of Hong Kong; Renmin University of China
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2025.2471054
发表日期：
2025
关键词：
nonconcave penalized likelihood
tuning-free robust
U-statistics
confidence-intervals
quantile regression
variable selection
efficient approach
tests
regions
摘要：
High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of the rank loss brings great challenges to the computation. To solve this critical issue, high-dimensional convoluted rank regression has been recently proposed, introducing penalized convoluted rank regression estimators. However, these developed estimators cannot be directly used to make inference. In this article, we investigate the statistical inference problem of high-dimensional convoluted rank regression. The use of U-statistic in convoluted rank loss function presents challenges for the analysis. We begin by establishing estimation error bounds of the penalized convoluted rank regression estimators under weaker conditions on the predictors. Building on this, we further introduce a debiased estimator and provide its Bahadur representation. Subsequently, a high-dimensional Gaussian approximation for the maximum deviation of the debiased estimator is derived, which allows us to construct simultaneous confidence intervals. For implementation, a novel bootstrap procedure is proposed and its theoretical validity is also established. Finally, simulation and real data analysis are conducted to illustrate the merits of our proposed methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.