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Simultaneous test procedures in terms of p-value copulae


  • Thorsten Dickhaus
  • Jakob Gierl


At least since [1], a broad class of multiple comparison procedures, so-called simultaneous test procedures (STPs), is established in the statistical literature. Elements of an STP are a testing family, consisting of a set of null hypotheses and corresponding test statistics, and a common critical constant. The latter threshold with which each of the test statistics has to be compared is calculated under the (joint) intersection hypothesis of all nulls. Under certain structural assumptions, the so-constructed STP provides strong control of the family-wise error rate. More recently, a general method to construct STPs in the case of asymptotic (joint) normality of the family of test statistics has been developed in [2], and numerical solutions to compute the critical constant in such cases were provided. Here, we propose to look at the problem from a different perspective. We will show that the threshold can equivalently be expressed by a quantile of the copula of the family of pvalues associated with the test statistics, assuming that each of these p-values is marginally uniformly distributed on the unit interval under the corresponding null hypothesis. This offers the opportunity to exploit the rich and growing literature on copula-based modeling of multivariate dependency structures for multiple testing problems and in particular for the construction of STPs in non-Gaussian situations.

Suggested Citation

  • Thorsten Dickhaus & Jakob Gierl, 2012. "Simultaneous test procedures in terms of p-value copulae," SFB 649 Discussion Papers SFB649DP2012-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2012-049

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    References listed on IDEAS

    1. Cerqueti, Roy & Costantini, Mauro & Lupi, Claudio, 2012. "A copula-based analysis of false discovery rate control under dependence assumptions," Economics & Statistics Discussion Papers esdp12065, University of Molise, Dept. EGSeI.
    2. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
    3. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    4. Christian Genest & Michel Gendron & Michaël Bourdeau-Brien, 2009. "The Advent of Copulas in Finance," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 609-618.
    5. Ghosal, Subhashis & Roy, Anindya, 2011. "Predicting False Discovery Proportion Under Dependence," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1208-1218.
    6. Wolfgang Härdle & Ostap Okhrin, 2009. "De copulis non est disputandum - Copulae: An Overview," SFB 649 Discussion Papers SFB649DP2009-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    More about this item


    distributional transform; family-wise error rate; multiple hypotheses testing; multiplicity correction; simultaneous statistical inference; single-step test factor structure; prediction;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory


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