Representations of multivariate normal distributions with special correlation structures

Six, F. B.

doi:10.1080/03610928108828111

Cited by 8 publications

(2 citation statements)

References 17 publications

(14 reference statements)

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“…For the multivariate normal distribution, such a factorization is almost trivial, and Curnow and Dunnett (1962) or Gupta (1963) showed that a simple calculation of the distribution is possible when the correlation is positive multiplicative. Six (1981) extended their results to the case of negative multiplicative correlation. The following theorem gives us a general factorization theorem for positive and negative multiplicative correlations.…”

Section: Characterizationsmentioning

confidence: 91%

Multiplicative Correlations

Baba

Shibata

2006

Ann Inst Stat Math

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Section: Characterizationsmentioning

confidence: 91%

Multiplicative Correlations

Baba

Shibata

2006

Ann Inst Stat Math

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“…For validating and comparing the MC and ME algorithms it is important to have a source of independently determined values of the MVN distribution against which to compare the approximations returned by each algorithm. For many purposes it may be sufficient to refer to tables of the MVN distribution that have been generated for special cases of the correlation matrix [15,18,[47][48][49][50][51]. Here, however, as in similar numerical studies [1,8,14,41], values of the MVN distribution were computed independently for correlation matrices defined by…”

Section: Test Problemsmentioning

confidence: 99%

Genz and Mendell-Elston Estimation of the High-Dimensional Multivariate Normal Distribution

et al. 2021

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Statistical analysis of multinomial data in complex datasets often requires estimation of the multivariate normal (mvn) distribution for models in which the dimensionality can easily reach 10–1000 and higher. Few algorithms for estimating the mvn distribution can offer robust and efficient performance over such a range of dimensions. We report a simulation-based comparison of two algorithms for the mvn that are widely used in statistical genetic applications. The venerable Mendell-Elston approximation is fast but execution time increases rapidly with the number of dimensions, estimates are generally biased, and an error bound is lacking. The correlation between variables significantly affects absolute error but not overall execution time. The Monte Carlo-based approach described by Genz returns unbiased and error-bounded estimates, but execution time is more sensitive to the correlation between variables. For ultra-high-dimensional problems, however, the Genz algorithm exhibits better scale characteristics and greater time-weighted efficiency of estimation.

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Orthant Probabilities

Owen¹

2004

Encyclopedia of Statistical Sciences

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Representations of multivariate normal distributions with special correlation structures

Cited by 8 publications

References 17 publications

Multiplicative Correlations

Multiplicative Correlations

Genz and Mendell-Elston Estimation of the High-Dimensional Multivariate Normal Distribution

Orthant Probabilities

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