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Exact testing with random permutations

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  • Jesse Hemerik

    (Leiden University Medical Center)

  • Jelle Goeman

    (Leiden University Medical Center)

Abstract

When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods based on random permutations tend to be seen as approximate. There exists a very limited amount of literature on exact testing with random permutations, and only recently a thorough proof of exactness was given. In this paper, we provide an alternative proof, viewing the test as a “conditional Monte Carlo test” as it has been called in the literature. We also provide extensions of the result. Importantly, our results can be used to prove properties of various multiple testing procedures based on random permutations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-017-0571-1
    DOI: 10.1007/s11749-017-0571-1
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    References listed on IDEAS

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    1. Nicolai Meinshausen, 2006. "False Discovery Control for Multiple Tests of Association Under General Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 227-237, June.
    2. Phipson Belinda & Smyth Gordon K, 2010. "Permutation P-values Should Never Be Zero: Calculating Exact P-values When Permutations Are Randomly Drawn," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-16, October.
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    4. Aldo Solari & Livio Finos & Jelle J. Goeman, 2014. "Rotation-based multiple testing in the multivariate linear model," Biometrics, The International Biometric Society, vol. 70(4), pages 954-961, December.
    5. Dennis D. Cox & Jong Soo Lee, 2008. "Pointwise testing with functional data using the Westfall--Young randomization method," Biometrika, Biometrika Trust, vol. 95(3), pages 621-634.
    6. Fortunato Pesarin, 2015. "Some Elementary Theory of Permutation Tests," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(22), pages 4880-4892, November.
    7. Nicolai Meinshausen & Peter Buhlmann, 2005. "Lower bounds for the number of false null hypotheses for multiple testing of associations under general dependence structures," Biometrika, Biometrika Trust, vol. 92(4), pages 893-907, December.
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    Cited by:

    1. 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.
    2. Djogbenou, Antoine & Sufana, Razvan, 2024. "Tests for group-specific heterogeneity in high-dimensional factor models," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    3. Hediger, Simon & Michel, Loris & Näf, Jeffrey, 2022. "On the use of random forest for two-sample testing," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    4. Angel G. Angelov & Magnus Ekström, 2023. "Tests of stochastic dominance with repeated measurements data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 443-467, September.
    5. Jesse Hemerik & Jelle J. Goeman, 2021. "Another Look at the Lady Tasting Tea and Differences Between Permutation Tests and Randomisation Tests," International Statistical Review, International Statistical Institute, vol. 89(2), pages 367-381, August.
    6. Jesse Hemerik & Jelle J. Goeman & Livio Finos, 2020. "Robust testing in generalized linear models by sign flipping score contributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 841-864, July.

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