An adaptive decorrelation procedure for signal detection

In global testing, where a large number of pointwise test statistics are aggregated to simultaneously test for a collection of null hypotheses, the handling of dependence is a crucial issue. In various fields, more particularly in genetic epidemiology and functional data analysis, many testing methods for detecting an association signal between a response and explanatory variables have been proposed. Some aggregation procedures ignore dependence across pointwise test statistics whereas others introduce a model for decorrelation, with unclear conclusions on their relative performance. Indeed, the benefit that can be expected from decorrelation highly depends on the interplay between the structure of dependence across pointwise test statistics and the pattern of the association signal. Within a large class of test statistics covering a continuum of decorrelation approaches, an optimal procedure is introduced. This procedure is based on the maximization of an ad-hoc cumulant generating function-based distance between the null and nonnull distributions of a global test statistic, in order to adapt the aggregation of the pointwise statistics to the pattern of the association signal. A comparative study including simulations and applications to genetic association studies demonstrates that the ability of this test to detect a signal is more robust to the dependence structure than existing methods.