Multiple Testing under Copula Dependency Structures

Abstract

The key to multiple testing is to respect the dependencies between the marginal hypotheses tests. Any dependency structure can be modeled by so-called copula functions. This makes copulas an interesting tool in multiple testing. In particular, it is possible to explicitly utilize the dependency structure of the data. This leads to the sub-class of copula-based multiple tests. One family of non-parametric copula estimators is constituted by Bernstein copulas. We extend previous statistical results regarding bivariate Bernstein copulas and study their impact on multiple tests. A related topic is the estimation of the proportion of true null hypotheses pi 0. It is a well known result in multiple hypothesis testing that this proportion is not identified under general dependencies. However, it is possible to estimate pi 0 if structural information about the dependency structure among the p-values is available.