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August 2007 Dependency and false discovery rate: Asymptotics
Helmut Finner, Thorsten Dickhaus, Markus Roters
Ann. Statist. 35(4): 1432-1455 (August 2007). DOI: 10.1214/009053607000000046

Abstract

Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when $n$ tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of $p$-values. In a general setup we present a series of results concerning the interrelation of Simes’ rejection curve and the (limiting) empirical distribution function of the $p$-values. Main objects under investigation are largest (limiting) crossing points between these functions, which play a key role in deriving explicit formulas for EER and FDR. As specific examples we investigate equi-correlated normal and $t$-variables in more detail and compute the limiting EER and FDR theoretically and numerically. A surprising limit behavior occurs if these models tend to independence.

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Helmut Finner. Thorsten Dickhaus. Markus Roters. "Dependency and false discovery rate: Asymptotics." Ann. Statist. 35 (4) 1432 - 1455, August 2007. https://doi.org/10.1214/009053607000000046

Information

Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1125.62076
MathSciNet: MR2351092
Digital Object Identifier: 10.1214/009053607000000046

Subjects:
Primary: 62F05 , 62J15
Secondary: 60F99 , 62F03

Keywords: exchangeable test statistics , expected error rate , False discovery rate , Glivenko–Cantelli theorem , largest crossing point , least favorable configurations , Multiple comparisons , multiple test procedure , multivariate total positivity of order 2 , positive regression dependency , Simes’ test

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 4 • August 2007
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