Two-sample testing of high-dimensional linear regression coefficients via complementary sketching

Gao, Fengnan and Wang, Tengyao ORCID: 0000-0003-2072-6645 (2022) Two-sample testing of high-dimensional linear regression coefficients via complementary sketching. Annals of Statistics. ISSN 0090-5364

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Abstract

We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and response vectors along directions that are complementary in sign in a subset of the coordinates, a process which we call ‘complementary sketching’. The resulting projected covariates and responses are aggregated to form two test statistics, which are shown to have essentially optimal asymptotic power under a Gaussian design when the difference between the two regression coefficients is sparse and dense respectively. Simulations confirm that our methods perform well in a broad class of settings and an application to a large single-cell RNA sequencing dataset demonstrates its utility in the real world.

Item Type:	Article
Additional Information:	© 2022 Institute of Mathematical Statistics.
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	25 Jul 2022 10:24
Last Modified:	12 Dec 2024 03:09
URI:	http://eprints.lse.ac.uk/id/eprint/115644

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