An iterated integral representation for a multivariate normal integral having block covariance structure

Robert E. Bechhofer; Ajit C. Tamhane

doi:10.1093/biomet/61.3.615

An iterated integral representation for a multivariate normal integral having block covariance structure

Robert E. Bechhofer^*, Ajit C. Tamhane

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

It is shown that a km-variate normal probability integral over a rectangular region can be expressed as an iterated k-variate normal integral when the k sets of m variates each have a certain commonly realized block covariance structure. The latter representation is much easier to evaluate numerically than is the former. This result generalizes previous results for k= 1 of Dunnett & Sobel and Steck & Owen.

Original language	English (US)
Pages (from-to)	615-619
Number of pages	5
Journal	Biometrika
Volume	61
Issue number	3
DOIs	https://doi.org/10.1093/biomet/61.3.615
State	Published - Dec 1974

Keywords

Block covariance strucutre
Multivariate normal integral
Multivariate normal probabilities
Numerical integration
Ranking and selection procedures

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Agricultural and Biological Sciences (miscellaneous)
Agricultural and Biological Sciences(all)
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1093/biomet/61.3.615

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abstract = "It is shown that a km-variate normal probability integral over a rectangular region can be expressed as an iterated k-variate normal integral when the k sets of m variates each have a certain commonly realized block covariance structure. The latter representation is much easier to evaluate numerically than is the former. This result generalizes previous results for k= 1 of Dunnett & Sobel and Steck & Owen.",

keywords = "Block covariance strucutre, Multivariate normal integral, Multivariate normal probabilities, Numerical integration, Ranking and selection procedures",

author = "Bechhofer, {Robert E.} and Tamhane, {Ajit C.}",

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T1 - An iterated integral representation for a multivariate normal integral having block covariance structure

AU - Bechhofer, Robert E.

AU - Tamhane, Ajit C.

N1 - Funding Information: supported by the U.S. Army Research Office and the

PY - 1974/12

Y1 - 1974/12

N2 - It is shown that a km-variate normal probability integral over a rectangular region can be expressed as an iterated k-variate normal integral when the k sets of m variates each have a certain commonly realized block covariance structure. The latter representation is much easier to evaluate numerically than is the former. This result generalizes previous results for k= 1 of Dunnett & Sobel and Steck & Owen.

AB - It is shown that a km-variate normal probability integral over a rectangular region can be expressed as an iterated k-variate normal integral when the k sets of m variates each have a certain commonly realized block covariance structure. The latter representation is much easier to evaluate numerically than is the former. This result generalizes previous results for k= 1 of Dunnett & Sobel and Steck & Owen.

KW - Block covariance strucutre

KW - Multivariate normal integral

KW - Multivariate normal probabilities

KW - Numerical integration

KW - Ranking and selection procedures

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EP - 619

JO - Biometrika

JF - Biometrika

IS - 3

ER -

An iterated integral representation for a multivariate normal integral having block covariance structure

Abstract

Keywords

ASJC Scopus subject areas

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