期刊
ANNALS OF STATISTICS
卷 35, 期 4, 页码 1432-1455出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/009053607000000046
关键词
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
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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