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Averaging p-values under exchangeability

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  • Choi, Woohyun
  • Kim, Ilmun

Abstract

A classical result indicates that the arithmetic average of p-values multiplied by the factor of 2 is a valid p-value under arbitrary dependence among p-values. Moreover, this constant factor cannot be improved in general without additional assumptions. Given this classical result, we study the average of p-values under exchangeability, which is a natural generalization of the i.i.d. assumption. Somewhat surprisingly, we prove that exchangeability is not enough to improve the constant factor of 2. This negative result motivates us to explore other conditions under which it is possible to obtain a smaller constant factor. Finally, we discuss certain benefits of the average of p-values over the average of statistics in terms of statistical power and provide empirical results that verify our theoretical findings.

Suggested Citation

  • Choi, Woohyun & Kim, Ilmun, 2023. "Averaging p-values under exchangeability," Statistics & Probability Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:stapro:v:194:y:2023:i:c:s0167715222002619
    DOI: 10.1016/j.spl.2022.109748
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    References listed on IDEAS

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    1. Yaowu Liu & Jun Xie, 2020. "Cauchy Combination Test: A Powerful Test With Analytic p-Value Calculation Under Arbitrary Dependency Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 393-402, January.
    2. DiCiccio, Cyrus J. & DiCiccio, Thomas J. & Romano, Joseph P., 2020. "Exact tests via multiple data splitting," Statistics & Probability Letters, Elsevier, vol. 166(C).
    3. Rajen D. Shah & Peter Bühlmann, 2018. "Goodness‐of‐fit tests for high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 113-135, January.
    4. Jana Janková & Rajen D. Shah & Peter Bühlmann & Richard J. Samworth, 2020. "Goodness‐of‐fit testing in high dimensional generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 773-795, July.
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