Title: Valid and consistent adaptive multiple tests
Authors: Arnold Janssen - Heinrich-Heine University Duesseldorf (Germany) [presenting]
Marc Ditzhaus - Technical University of Dortmund (Germany)
Abstract: Simultaneous hypotheses testing for big data sets is a very difficult affair. First, the modern concept of multiple testing is introduced and examples are illustrated. Then, new results are presented. The pioneer multiple test, with up to date more than 42000 citations, is a basic tool in high dimensional data analysis, for instance in genomics, when a huge amount of tests are carried out simultaneously for the same data set. This test, and also improved data dependent adaptive tests, controls the so called FDR. The FDR is the expectation of the ratio of the number of false rejections and all rejections. Although the FDR can be controlled by some given level alpha, the false discovery proportion (FDP) may have stochastic fluctuations. We discuss the consistency for general adaptive multiple tests. We present finite sample and asymptotic results in order to bound deviations of the FDP from the present FDR level.