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

Robert E. Bechhofer*, Ajit C. Tamhane

*Corresponding author for this work

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)615-619
Number of pages5
JournalBiometrika
Volume61
Issue number3
DOIs
StatePublished - Dec 1 1974

Keywords

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

ASJC Scopus subject areas

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

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