Article contents
Optimal second-order product probability bounds
Published online by Cambridge University Press: 14 July 2016
Abstract
Let P(c) = P(X1 ≦ c1, · ··, Xp ≦ cp) for a random vector (X1, · ··, Xp). Bounds are considered of the form where T is a spanning tree corresponding to the bivariate probability structure and di is the degree of the vertex i in T. An optimized version of this inequality is obtained. The main result is that alwayṡ dominates certain second-order Bonferroni bounds. Conditions on the covariance matrix of a N(0,Σ) distribution are given so that this bound applies, and various applications are given.
Keywords
MSC classification
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1993
Footnotes
Research supported by NSA Grant No. MDA-904-90-H-4063 and by the Air Force Office of Scientific Research under Contract AFOSR 84-0113.
Research supported by NCI Grant No. 1-R01-CA54706-01, by the Air Force Office of Scientific Research under Contract AFOSR 84-0113, and by a seed grant from the Ohio State University.
References
- 6
- Cited by