Distributed Selective Inference for Quantile Regression
Abstract
We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized least-squares formulation, thereby facilitating distributed selective inference. For valid post-selection inference, a randomized procedure is introduced, in which the Lasso selection event is characterized through the associated Karush-Kuhn-Tucker conditions and the conditional distribution of the aggregated estimator is derived given the selection event. The resulting algorithm requires only three rounds of communication between local machines and the central server. Under standard regularity conditions, we establish the asymptotic validity of the proposed procedure and develop a large-deviation approximation to the selective likelihood for computationally tractable implementation. Simulation studies and a real-data application demonstrate the satisfactory finite-sample performance of the proposed method.
Related
- Clouded Representatives and Score Matching for Distributed Quantile Regression
- Heterogeneity-calibrated Byzantine-robust distributed composite quantile regression
- Quantile-Only Regression: Inference and Partial Identification under Quantile Disclosure
- Bias Correction and Inference for Panel Quantile Regression
- Statistical inference for quantile correlation regression with bivariate outcomes
BibTeX
@misc{yuan2026distributed,
title = {{Distributed Selective Inference for Quantile Regression}},
author = {Xiaohui Yuan and Jiahan Teng and Yan Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.13311},
eprint = {2608.13311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13311},
}
RIS
TY - UNPB
TI - Distributed Selective Inference for Quantile Regression
AU - Xiaohui Yuan
AU - Jiahan Teng
AU - Yan Zhou
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2608.13311
UR - https://arxiv.org/abs/2608.13311
AB - We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized least-squares formulation, thereby facilitating distributed selective inference. For valid post-selection inference, a randomized procedure is introduced, in which the Lasso selection event is characterized through the associated Karush-Kuhn-Tucker conditions and the conditional distribution of the aggregated estimator is derived given the selection event. The resulting algorithm requires only three rounds of communication between local machines and the central server. Under standard regularity conditions, we establish the asymptotic validity of the proposed procedure and develop a large-deviation approximation to the selective likelihood for computationally tractable implementation. Simulation studies and a real-data application demonstrate the satisfactory finite-sample performance of the proposed method.
ER -