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Distribution of the Harmonic Mean of P-values with Application to Multiple Testing

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  • Jiangtao Gou

    (Villanova University)

  • Ajit C. Tamhane

    (Northwestern University)

Abstract

In this paper we analyze the null distribution of the harmonic mean of i.i.d. P-values, each distributed as U[0, 1]. We derive the exact distribution numerically for small n using the convolution method and asymptotic distribution for large n. We show that the critical constants computed using the exact distribution and the asymptotic distribution match fairly well. We construct a procedure based on the harmonic means of P-value for testing multiple hypotheses using the closure principle (Marcus et al., Biometrika, 63, 655–660, 1976). We show via simulation that our proposed HMP procedure is generally more powerful than several other P-value based procedures including the Holm (Scandinavian Journal of Statistics, 6, 65–70, 1979), Hochberg (Biometrika, 75, 800–802, 1988), Hommel (Biometrika, 75, 383–386, 1988) and the Hochberg-Hommel hybrid procedure (Gou et al., Biometrika, 101, 899–911, 2014) under independence as well as under dependence (both positive and negative). It can be implemented using a simple R code.

Suggested Citation

  • Jiangtao Gou & Ajit C. Tamhane, 2025. "Distribution of the Harmonic Mean of P-values with Application to Multiple Testing," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(1), pages 1-28, May.
    • Handle: RePEc:spr:sankhb:v:87:y:2025:i:1:d:10.1007_s13571-025-00358-y
    DOI: 10.1007/s13571-025-00358-y
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    References listed on IDEAS

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    1. Jiangtao Gou & Ajit C. Tamhane & Dong Xi & Dror Rom, 2014. "A class of improved hybrid Hochberg–Hommel type step-up multiple test procedures," Biometrika, Biometrika Trust, vol. 101(4), pages 899-911.
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