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Power enhancement of permutation-augmented partial-correlation tests via fixed-row permutations

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  • Wang, Tianyi
  • Wang, Guanghui
  • Wang, Zhaojun
  • Zou, Changliang

Abstract

Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate of interest. We remedy this by fixing a design-driven subset of rows and permuting only the remainder. The fixed rows are chosen by a greedy algorithm that maximizes a lower bound on power. This strategy reduces covariate-permutation collinearity while preserving worst-case Type I error control. Simulations confirm that this refinement maintains nominal size and delivers substantial power gains over original unrestricted permutations, especially in high-collinearity regimes.

Suggested Citation

  • Wang, Tianyi & Wang, Guanghui & Wang, Zhaojun & Zou, Changliang, 2026. "Power enhancement of permutation-augmented partial-correlation tests via fixed-row permutations," Statistics & Probability Letters, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:stapro:v:230:y:2026:i:c:s0167715225002366
    DOI: 10.1016/j.spl.2025.110591
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    References listed on IDEAS

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    1. Lihua Lei & Peter J Bickel, 2021. "An assumption-free exact test for fixed-design linear models with exchangeable errors [Rank tests of sub-hypotheses in the general linear regression]," Biometrika, Biometrika Trust, vol. 108(2), pages 397-412.
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    4. Jesse Hemerik & Jelle Goeman, 2018. "Exact testing with random permutations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 811-825, December.
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    6. Aaditya Ramdas & Rina Foygel Barber & Emmanuel J. Candès & Ryan J. Tibshirani, 2023. "Permutation Tests Using Arbitrary Permutation Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1156-1177, August.
    7. 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.
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