An approximation of multivariate normal orthant probabilities of dimension 4: A contingency-table approach

Yuchung J. Wang

doi:10.1080/03610918708812635

An approximation of multivariate normal orthant probabilities of dimension 4: A contingency-table approach

Yuchung J. Wang

Rutgers Camden, Mathematics

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

2 Scopus citations

Abstract

The collection of all orthant probabilities for a four-dimensional multivariate normal distribution can be considered as a 2x2x2x2 contingency table. There are no three-way interactions for the contingency table. And the fourth-order interaction is negligible. The six two-way marginal probabilities are sufficient statistics for approximating the 2⁴ orthant probabilities. The iterative proportional fitting algorithm is used to compute the four-dimensional contingency table from the six marginal 2x2 tables.

Original language	English (US)
Pages (from-to)	1039-1049
Number of pages	11
Journal	Communications in Statistics - Simulation and Computation
Volume	16
Issue number	4
DOIs	https://doi.org/10.1080/03610918708812635
State	Published - Jan 1 1987

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation

Keywords

cross-product ratio
interactions
iterative proportional fitting algorithm
log-linear model

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10.1080/03610918708812635

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AB - The collection of all orthant probabilities for a four-dimensional multivariate normal distribution can be considered as a 2x2x2x2 contingency table. There are no three-way interactions for the contingency table. And the fourth-order interaction is negligible. The six two-way marginal probabilities are sufficient statistics for approximating the 24 orthant probabilities. The iterative proportional fitting algorithm is used to compute the four-dimensional contingency table from the six marginal 2x2 tables.

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KW - log-linear model

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An approximation of multivariate normal orthant probabilities of dimension 4: A contingency-table approach

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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