## The Annals of Statistics

### Some probability inequalities for ordered $\rm MTP\sb 2$ random variables: a proof of the Simes conjecture

Sanat K. Sarkar

#### Abstract

Some new probability inequalities involving the ordered components of an $MTP_2$ random vector are derived, which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing. This conjecture has been mostly validated so far using simulation.

#### Article information

Source
Ann. Statist., Volume 26, Number 2 (1998), 494-504.

Dates
First available in Project Euclid: 31 July 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1028144846

Digital Object Identifier
doi:10.1214/aos/1028144846

Mathematical Reviews number (MathSciNet)
MR1626047

Zentralblatt MATH identifier
0929.62065

#### Citation

Sarkar, Sanat K. Some probability inequalities for ordered $\rm MTP\sb 2$ random variables: a proof of the Simes conjecture. Ann. Statist. 26 (1998), no. 2, 494--504. doi:10.1214/aos/1028144846. https://projecteuclid.org/euclid.aos/1028144846

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