Simultaneous false discovery proportion bounds via knockoffs and closed testing

Journal of the Royal Statistical Society Series B (Statistical Methodology), vol. 86, pp. 966–986

Abstract

Abstract We propose new methods to obtain simultaneous false discovery proportion bounds for knockoff-based approaches. We first investigate an approach based on Janson and Su’s k-familywise error rate control method and interpolation. We then generalize it by considering a collection of k values, and show that the bound of Katsevich and Ramdas is a special case of this method and can be uniformly improved. Next, we further generalize the method by using closed testing with a multi-weighted-sum local test statistic. This allows us to obtain a further uniform improvement and other generalizations over previous methods. We also develop an efficient shortcut for its implementation. We compare the performance of our proposed methods in simulations and apply them to a data set from the UK Biobank.

Authors 3

1. Jinzhou Li corresponding

   Stanford University

   Affiliation as printed

   Department of Statistics, Stanford University , Stanford, CA , USA

2. Marloes H. Maathuis

   ETH Zurich · Seminar for Statistics

   Affiliation as printed

   Seminar für Statistik, ETH Zürich, Zürich , Switzerland

3. Jelle J. Goeman Aachen Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Biomedical Data Sciences, Leiden University Medical Center , Leiden , The Netherlands