Testing high-dimensional regression coefficients in linear models

This paper is concerned with statistical inference for regression coefficients in high-dimensional linear regression models. We propose a new method for testing the coefficient vector of the high-dimensional linear models, and establish the asymptotic normality of our proposed test statistic with the aid of the martingale central limit theorem. We derive the asymptotical relative efficiency (ARE) of the proposed test with respect to the test proposed in Zhong and Chen and show that the ARE is always greater or equal to one under the local alternative studied in this paper. Our numerical studies imply that the proposed test with critical values derived from its asymptotical normal distribution may retain Type I error rate very well. Our numerical comparison demonstrates the proposed test performs better than existing ones in terms of powers. We further illustrate our proposed method with a real data example.

Find the version of record at https://doi.org/10.1214/24-AOS2420

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Work Title Testing high-dimensional regression coefficients in linear models
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Open Access
Creators
  1. Alex Zhao
  2. Changcheng Li
  3. Runze Li
  4. Zhe Zhang
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Annals of Statistics
Publication Date October 1, 2024
Publisher Identifier (DOI)
  1. https://doi.org/10.1214/24-AOS2420
Deposited January 29, 2025

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  • Added 24-AOS2420-1.pdf
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  • Added Creator Changcheng Li
  • Added Creator Runze Li
  • Added Creator Zhe Zhang
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