M-matrices as covariance matrices of multinormal distributions

DOI10.1016/0024-3795(83)80027-5zbMath0538.62040OpenAlexW2062814521MaRDI QIDQ793463

Yosef Rinott, Samuel Karlin

Publication date: 1983

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(83)80027-5

zbMATH Keywords

canonical correlationM-matricesinverse covariance matrixmultivariate normal densitiespartial correlation coefficients

Mathematics Subject Classification ID

Measures of association (correlation, canonical correlation, etc.) (62H20) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Characterization and structure theory of statistical distributions (62E10) Hermitian, skew-Hermitian, and related matrices (15B57)

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Cites Work

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• Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen
• Topological proofs for certain theorems on matrices with non-negative elements
• Iterative solution of linear systems of functional equations
• Schur complements and statistics
• Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions
• Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions
• Total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities
• Positively correlated normal variables are associated
• Correlation inequalities on some partially ordered sets
• Positive dependence of the bivariate and trivariate absolute normal, \(t,\chi^2\), and \(F\) distributions
• Association and probability inequalities
• Negative association of random variables, with applications
• Association of normal random variables and Slepian's inequality
• Some matrix inequalities
• Events which are almost independent
• NOTE ON M-MATRICES
• Identification of noisy systems
• Association of Random Variables, with Applications
• A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS