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.
Keywords
MathematicsConjectureRandom variableField (mathematics)InequalityCombinatoricsPure mathematicsDiscrete mathematicsStatisticsMathematical analysis
Related Publications
Local Maxima and the Expected Euler Characteristic of Excursion Sets of <i>χ <sup>2</sup>, F</i> and <i>t</i> Fields
The maximum of a Gaussian random field was used by Worsley et al. (1992) to test for activation at an unknown point in positron emission tomography images of blood flow in the h...
The Capacity of Linear Channels with Additive Gaussian Noise
The standard method of computing the mutual information between two stochastic processes with finite energy replaces the processes with their Fourier coefficients. This procedur...
Publication Info
- Year
- 1998
- Type
- article
- Volume
- 26
- Issue
- 2
- Citations
- 244
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
244
OpenAlex
Cite This
Sanat K. Sarkar
(1998).
Some probability inequalities for ordered $\rm MTP\sb 2$ random variables: a proof of the Simes conjecture.
The Annals of Statistics
, 26
(2)
.
https://doi.org/10.1214/aos/1028144846
Identifiers
- DOI
- 10.1214/aos/1028144846