B0818
Title: Multiple hypothesis testing in multivariate copula models
Authors: Thorsten Dickhaus - University of Bremen (Germany) [presenting]
Abstract: We are concerned with simultaneous testing of a family of null hypotheses under a single statistical model. We assume that the individual tests are carried out by means of (marginal) $p-$values and that these $p-$values, regarded as random variables, are dependent. Two popular type I error measures in multiple testing are the family-wise error rate (FWER) and the false discovery rate (FDR). Firstly, we express the threshold of an FWER-controlling simultaneous test procedure (STP) in terms of the copula function of the family of $p-$values, 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 literature on copula-based modeling of multivariate dependency structures for the construction of STPs in non-Gaussian situations. The second part deals with Archimedean copulae in multiple testing in the case that the distributional transforms of the $p-$values are elements of a sequence of exchangeable random variables. We utilize analytic properties of Archimedean copulae to derive sharp bounds for the FDR of the linear step-up test for such $p-$values.
