False discovery rate control for non-positively regression dependent test statistics

In this paper we present a modification of the Benjamini and Hochberg false discovery rate controlling procedure for testing non-positive dependent test statistics. The new testing procedure makes use of the same series of linearly increasing critical values. Yet, in the new procedure the set of p-values is divided into subsets of positively dependent p-values, and each subset of p-values is separately sorted and compared to the series of critical values. In the first part of the paper we introduce the new testing methodology, discuss the technical issues needed to apply the new approach, and apply it to data from a genetic experiment.