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Residual permutation test for regression coefficient testing

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  • Wen, Kaiyue
  • Wang, Tengyao
  • Wang, Yuhao

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

Suggested Citation

  • Wen, Kaiyue & Wang, Tengyao & Wang, Yuhao, 2025. "Residual permutation test for regression coefficient testing," LSE Research Online Documents on Economics 126275, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:126275
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    References listed on IDEAS

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

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