Simultaneous test procedures in terms of p-value copulae
At least since , 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 , 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.
|Date of creation:||Aug 2012|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://sfb649.wiwi.hu-berlin.deEmail:
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Matthias R. Fengler & Ostap Okhrin, 2012.
SFB 649 Discussion Papers
SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Christian Genest & Michel Gendron & Micha�l Bourdeau-Brien, 2009. "The Advent of Copulas in Finance," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 609-618.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:hum:wpaper:sfb649dp2012-049. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RDC-Team)
If references are entirely missing, you can add them using this form.