Residual permutation test for regression coefficient testing

Kaiyue Wen, Tengyao Wang and Yuhao Wang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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

Keywords: distribution-free test; permutation test; finite-population validity; heavy tail distribution; high-dimensional data (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2025-04-30
New Economics Papers: this item is included in nep-ecm and nep-ets
References: Add references at CitEc
Citations:

Published in Annals of Statistics, 30, April, 2025, 53(2), pp. 724 - 748. ISSN: 0090-5364

Downloads: (external link)
http://eprints.lse.ac.uk/126275/ Open access version. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:126275

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().