PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On the False Discovery Rate and an Asymptotically Optimal Rejection Curve
Helmut Finner, Thorsten Dickhaus and Markus Roters
The Annals of Statistics Volume 37, Number 2, pp. 596-618, 2009. ISSN 0090-5364

Abstract

In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation for this new curve and propose some procedures related to it. Then we introduce a set of possible assumptions and give a unifying short proof of FDR control for procedures based on Simes’ critical values, whereby certain types of dependency are allowed. This methodology of proof is then applied to other fixed rejection curves including the proposed new curve. Among others, we investigate the problem of finding least favorable parameter configurations such that the FDR becomes largest. We then derive a series of results concerning asymptotic FDR control for procedures based on the new curve and discuss several example procedures in more detail. A main result will be an asymptotic optimality statement for various procedures based on the new curve in the class of fixed rejection curves. Finally, we briefly discuss strict FDR control for a finite number of hypotheses.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:6797
Deposited By:Thorsten Dickhaus
Deposited On:08 March 2010