PROCEDURES CONTROLLING THE k-FDR USING BIVARIATE DISTRIBUTIONS OF THE NULL p-VALUES

Procedures controlling error rates measuring at least k false rejections, instead of at least one, are often desired while testing a large number of hypotheses. The k-FWER, probability of at least k false rejections, is such an error rate that has been introduced, and procedures controlling it have been proposed. Recently, Sarkar (2007) introduced an alternative, less conservative notion of error rate, the k-FDR, generalizing the usual notion of false discovery rate (FDR), and proposed a procedure controlling it based on the k-dimensional joint distributions of the null p-values and assuming MTP2 (multivariate totally positive of order two) positive dependence among all the p-values. In this article, we assume a less restrictive form of positive dependence than MTP2, and develop alternative procedures based only on the bivariate distributions of the null p-values.