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Sarkar, Sanat K.

Some probability inequalities for ordered MTP\(_2\) random variables: a proof of the Simes conjecture. (English) Zbl 0929.62065

Ann. Stat. 26, No. 2, 494-504 (1998).
Summary: Some new probability inequalities involving the ordered components of a multivariate totally positive of order 2 \((\text{MTP}_2)\) random vector are derived, which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing. This conjecture of R. J. Simes [Biometrika 73, 751-754 (1986; Zbl 0613.62067)] has been mostly validated so far using simulation.

Cited in 1 Review
Cited in 71 Documents

MSC:

62H15 Hypothesis testing in multivariate analysis
60E15 Inequalities; stochastic orderings
62H99 Multivariate analysis

Keywords:

P-values; Simes test; positive dependence; multivariate totally positive of order 2

Citations:

Zbl 0613.62067
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Full Text: DOI

References:

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