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Zbl 0912.62079
Sarkar, Sanat K.; Chang, Chung-Kuei
The Simes method for multiple hypothesis testing with positively dependent test statistics. (English)
[J] J. Am. Stat. Assoc. 92, No.440, 1601-1608 (1997). ISSN 0162-1459; ISSN 1537-274X/e

Summary: The Simes method [{\it R. J. Simes}, Biometrika 73, 751-754 (1986; Zbl 0613.62067)] for testing intersection of more than two hypotheses is known to control the probability of type I error only when the underlying test statistics are independent. Although this method is more powerful than the classical Bonferroni method, it is not known whether it is conservative when the test statistics are dependent. This article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple-hypothesis testing situations, the Simes method indeed controls the probability of type I error. This extends some results established very recently in the special case of two hypotheses.

MSC 2000:: *62J15 Multiple comparisons
62H99 Multivariate analysis

Keywords: control of probability of type I error; order statistics; totally positive of order 2 densities; Simes method; Bonferroni method

Citations: Zbl 0613.62067

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