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Optimal second-order product probability bounds

Part of: Multivariate analysis

Published online by Cambridge University Press:  14 July 2016

Henry W. Block ,
Timothy M. Costigan  and
Allan R. Sampson
Henry W. Block*
Affiliation:
University of Pittsburgh
Timothy M. Costigan*
Affiliation:
The Ohio State University
Allan R. Sampson*
Affiliation:
University of Pittsburgh
*
∗ Postal address: Department of Mathematics and Statistics, University of Pittsburgh, PA 15260, USA.
∗∗ Postal address: Department of Statistics, The Ohio State University, 141 Cockins Hall, Columbus, OH 43210-1247, USA.
∗ Postal address: Department of Mathematics and Statistics, University of Pittsburgh, PA 15260, USA.
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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

PRODUCT BOUNDSSECOND-ORDER BOUNDSBONFERRONI BOUNDSMTP2PARTIAL CORRELATIONPOSITIVE DEPENDENCEGRAPH THEORYCHANGE POINTSIMULTANEOUS INFERENCE

MSC classification

Primary: 62H05: Characterization and structure theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 675 - 691
Copyright
Copyright © Applied Probability Trust 1993 

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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.

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