Residual permutation test for regression coefficient testing

Wen, Kaiyue, Wang, Tengyao ORCID: 0000-0003-2072-6645 and Wang, Yuhao (2024) Residual permutation test for regression coefficient testing. Annals of Statistics. ISSN 0090-5364 (In Press)

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Abstract

We consider the problem of testing whether a single coefficient is equal to zero in linear models when the dimension of covariates p can be up to a constant fraction of sample size n. In this regime, an important topic is to propose tests with finite-population valid size control without requiring the noise to follow strong distributional assumptions. In this paper, we propose a new method, called residual permutation test (RPT), which is constructed by projecting the regression residuals onto the space orthogonal to the union of the column spaces of the original and permuted design matrices. RPT can be proved to achieve finite-population size validity under fixed design with just exchangeable noises, whenever p < n=2. Moreover, RPT is shown to be asymptotically powerful for heavy tailed noises with bounded (1 + t)-th order moment when the true coefficient is at least of order nt=(1+t) for t 2 [0; 1]. We further proved that this signal size requirement is essentially rate-optimal in the minimax sense. Numerical studies confirm that RPT performs well in a wide range of simulation settings with normal and heavy-tailed noise distributions.

Item Type:	Article
Additional Information:	© 2024
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	06 Dec 2024 16:45
Last Modified:	12 Dec 2024 04:36
URI:	http://eprints.lse.ac.uk/id/eprint/126275

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