The Annals of Statistics
- Ann. Statist.
- Volume 35, Number 4 (2007), 1432-1455.
Dependency and false discovery rate: Asymptotics
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.
Ann. Statist., Volume 35, Number 4 (2007), 1432-1455.
First available in Project Euclid: 29 August 2007
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Zentralblatt MATH identifier
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
Finner, Helmut; Dickhaus, Thorsten; Roters, Markus. Dependency and false discovery rate: Asymptotics. Ann. Statist. 35 (2007), no. 4, 1432--1455. doi:10.1214/009053607000000046. https://projecteuclid.org/euclid.aos/1188405617