Title: Multivariate multiple test procedures based on nonparametric copula estimation
Authors: Andre Neumann - University of Bremen (Germany)
Taras Bodnar - Stockholm University (Sweden)
Dietmar Pfeifer - Carl von Ossietzky University of Oldenburg (Germany)
Thorsten Dickhaus - University of Bremen (Germany) [presenting]
Abstract: Multivariate multiple test procedures have received growing attention recently. This is due to the fact that data generated by modern applications typically are high-dimensional, but possess pronounced dependencies due to the technical mechanisms involved in the experiments. Hence, it is possible and often necessary to exploit these dependencies in order to achieve reasonable power. We express dependency structures in the most general manner, namely, by means of copula functions. One class of nonparametric copula estimators is constituted by Bernstein copulae. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests. In particular, we utilize them to derive asymptotic confidence regions for the family-wise error rate (FWER) of simultaneous test procedures which are empirically calibrated by making use of Bernstein copulae approximations of the dependency structure among the test statistics. A simulation study quantifies the gain in FWER level exhaustion and, consequently, power which can be achieved by exploiting the dependencies, in comparison with common threshold calibrations like the Bonferroni or Sidak corrections. Finally, we demonstrate an application of the proposed methodology to real-life data from insurance.