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

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  • Gao, Fengnan
  • Wang, Tengyao

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.

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  • Gao, Fengnan & Wang, Tengyao, 2022. "Two-sample testing of high-dimensional linear regression coefficients via complementary sketching," LSE Research Online Documents on Economics 115644, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:115644
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    File URL: http://eprints.lse.ac.uk/115644/
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    Keywords

    high-dimensional data; linear model; minimax detection; sparsity; two-sample hypothesis testing;
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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