Adaptive Test Procedure for High Dimensional Regression Coefficient

We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging classical max-type and sum-type tests. We establish joint weak convergence of the extreme-value component and standardized $L$-statistics under mild conditions, yielding an asymptotic independence that justifies combining multiple $k$'s. An adaptive omnibus test is constructed via a Cauchy combination over a dyadic grid of $k$, and a wild bootstrap calibration is provided with theoretical guarantees. Simulations demonstrate accurate size and strong power across sparse and dense alternatives, including non-Gaussian designs.

• Publication year

  2026

• Venue

  Unknown venue

• Publication date

  2026-02-08

• Fields of study

  Mathematics

• Identifiers
  arXiv 2602.07911
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Kernel‐based marginal testing for covariate effects in high‐dimensional settings

  2026cited by this paper
• Adaptive L-statistics for high dimensional test problem

  2024influential reference
• Tests for high-dimensional generalized linear models under general covariance structure

  2024cited by this paper
• Asymptotic Independence of the Sum and Maximum of Dependent Random Variables with Applications to High-Dimensional Tests

  2022influential reference
• Testing the Effects of High-Dimensional Covariates via Aggregating Cumulative Covariances

  2022cited by this paper
• Maximum-type tests for high-dimensional regression coefficients using Wilcoxon scores

  2021cited by this paper
• A new nonparametric test for high-dimensional regression coefficients

  2017cited by this paper
• Robust U-type test for high dimensional regression coefficients using refitted cross-validation variance estimation

  2016cited by this paper
• Rank-based score tests for high-dimensional regression coefficients

  2013cited by this paper
• Testing covariates in high-dimensional regression

  2013cited by this paper
• Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control

  2011cited by this paper
• Tests for High-Dimensional Regression Coefficients With Factorial Designs

  2011cited by this paper
• Testing against a high dimensional alternative

  2006influential reference

• No citing papers are available for this paper.