Adaptive Test for High Dimensional Quantile Regression

Fuente: arXiv
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Main Authors: Zhao, Ping, Liu, Zhenyu, Zhuang, Dan
Format: Preprint
Published: 2025
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author Zhao, Ping
Liu, Zhenyu
Zhuang, Dan
author_facet Zhao, Ping
Liu, Zhenyu
Zhuang, Dan
contents Testing high-dimensional quantile regression coefficients is crucial, as tail quantiles often reveal more than the mean in many practical applications. Nevertheless, the sparsity pattern of the alternative hypothesis is typically unknown in practice, posing a major challenge. To address this, we propose an adaptive test that remains powerful across both sparse and dense alternatives.We first establish the asymptotic independence between the max-type test statistic proposed by \citet{tang2022conditional} and the sum-type test statistic introduced by \citet{chen2024hypothesis}. Building on this result, we propose a Cauchy combination test that effectively integrates the strengths of both statistics and achieves robust performance across a wide range of sparsity levels. Simulation studies and real data applications demonstrate that our proposed procedure outperforms existing methods in terms of both size control and power.
format Preprint
id arxiv_https___arxiv_org_abs_2512_21541
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Adaptive Test for High Dimensional Quantile Regression
Zhao, Ping
Liu, Zhenyu
Zhuang, Dan
Methodology
Testing high-dimensional quantile regression coefficients is crucial, as tail quantiles often reveal more than the mean in many practical applications. Nevertheless, the sparsity pattern of the alternative hypothesis is typically unknown in practice, posing a major challenge. To address this, we propose an adaptive test that remains powerful across both sparse and dense alternatives.We first establish the asymptotic independence between the max-type test statistic proposed by \citet{tang2022conditional} and the sum-type test statistic introduced by \citet{chen2024hypothesis}. Building on this result, we propose a Cauchy combination test that effectively integrates the strengths of both statistics and achieves robust performance across a wide range of sparsity levels. Simulation studies and real data applications demonstrate that our proposed procedure outperforms existing methods in terms of both size control and power.
title Adaptive Test for High Dimensional Quantile Regression
topic Methodology
url https://arxiv.org/abs/2512.21541