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Compound p-value statistics for multiple testing procedures

Author

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  • Habiger, Joshua D.
  • Peña, Edsel A.

Abstract

Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently been shown that these types of multiple testing procedures are inefficient since such p-values do not depend upon all of the available data. This paper provides tools for constructing compoundp-value statistics, which are those that depend upon all of the available data, but still satisfy the conditions of independence and uniformity under the null hypotheses. Several examples are provided, including a class of compound p-value statistics for testing location shifts. It is demonstrated, both analytically and through simulations, that multiple testing procedures tend to reject more false null hypotheses when applied to these compound p-values rather than the usual p-values, and at the same time still guarantee the desired type I error rate control. The compound p-values are used to analyze a real microarray data set and allow for more rejected null hypotheses.

Suggested Citation

  • Habiger, Joshua D. & Peña, Edsel A., 2014. "Compound p-value statistics for multiple testing procedures," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 153-166.
    • Handle: RePEc:eee:jmvana:v:126:y:2014:i:c:p:153-166
    DOI: 10.1016/j.jmva.2014.01.007
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    References listed on IDEAS

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    Cited by:

    1. Nikolaos Ignatiadis & Wolfgang Huber, 2021. "Covariate powered cross‐weighted multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 720-751, September.
    2. Edsel Peña & Joshua Habiger & Wensong Wu, 2015. "Classes of multiple decision functions strongly controlling FWER and FDR," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 563-595, July.

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