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<p>In this paper we analyze the null distribution of the harmonic mean of i.i.d. <i>P</i>-values, each distributed as <i>U</i>[0,&#xa0;1]. We derive the exact distribution numerically for small <i>n</i> using the convolution method and asymptotic distribution for large <i>n</i>. 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 <i>P</i>-value for testing multiple hypotheses using the closure principle (Marcus et al., <i>Biometrika</i>, <b>63</b>, 655–660, 1976). We show via simulation that our proposed HMP procedure is generally more powerful than several other <i>P</i>-value based procedures including the Holm (<i>Scandinavian Journal of Statistics</i>, <b>6,</b> 65–70, 1979), Hochberg (<i>Biometrika</i>, <b>75,</b> 800–802, 1988), Hommel (<i>Biometrika</i>, <b>75,</b> 383–386, 1988) and the Hochberg-Hommel hybrid procedure (Gou et al., <i>Biometrika</i>, <b>101,</b> 899–911, 2014) under independence as well as under dependence (both positive and negative). It can be implemented using a simple <Emphasis FontCategory="NonProportional">R</Emphasis> code.</p>

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

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  • 发表日期：

    2025年5月6日

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  • Jiangtao Gou,
  • Ajit C. Tamhane

摘要

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.