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Some permutation tests for high dimensional mean vectors

Author

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  • Caizhu Huang

    (Guandong University of Finance and Economics
    University of Padova)

  • Euloge Clovis Kenne Pagui

    (University of Oslo)

  • Fortunato Pesarin

    (University of Padova)

Abstract

For high dimensional data where the dimension p of the observation vector is larger than the group sample sizes $$n_i, i=1,2$$ n i , i = 1 , 2 , classical approaches based on asymptotic theory are no longer valid. A recent parametric projection test shows a comparable type I error but with a substantial power improvement. However, the asymptotic theory of all such statistics may not hold with small $$n_i$$ n i , especially, in the presence of strong correlation structures. We here propose the use of a permutation test based on the same parametric projection test statistic. Extensive simulation results show that the permutation versions are more accurate under the null hypothesis than the parametric projection test when sample sizes are small and, especially when there is a strong correlation in the data. A significant test of “Sell in May and Go Away” for the manufacturing sector in China’s A-share market from May 2001 to October 2017 illustrates its application.

Suggested Citation

  • Caizhu Huang & Euloge Clovis Kenne Pagui & Fortunato Pesarin, 2025. "Some permutation tests for high dimensional mean vectors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(4), pages 753-765, September.
    • Handle: RePEc:spr:stmapp:v:34:y:2025:i:4:d:10.1007_s10260-025-00804-1
    DOI: 10.1007/s10260-025-00804-1
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    References listed on IDEAS

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    1. Caizhu Huang & Xia Cui & Euloge Clovis Kenne Pagui, 2024. "Two-sample mean vector projection test in high-dimensional data," Computational Statistics, Springer, vol. 39(3), pages 1061-1091, May.
    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. 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.
    5. Sven Bouman & Ben Jacobsen, 2002. "The Halloween Indicator, "Sell in May and Go Away": Another Puzzle," American Economic Review, American Economic Association, vol. 92(5), pages 1618-1635, December.
    6. Federico Ferraccioli & Laura M. Sangalli & Livio Finos, 2023. "Nonparametric tests for semiparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 1106-1130, September.
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