Concentration inequalities for multivariate distributions. I: Multivariate normal distributions

DOI10.1016/0167-7152(91)90004-BzbMath0749.62036OpenAlexW2071822689MaRDI QIDQ1186631

Michael D. Perlman, Morris L. Eaton

Publication date: 28 June 1992

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(91)90004-b

zbMATH Keywords

invarianceconvex setssymmetry conditioncounterexamplesnon-convex setscovariance matricespositive definite covariance matrixefficiency comparisonsp-variate normal distributiongroup of orthogonal transformationsconvolution inequalitiesmultivariate concentration inequalitiesprobabilities of multivariate regions

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Foundations and philosophical topics in statistics (62A01)

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Multivariate dispersion orderings, Median balls: An extension of the interquantile intervals to multivariate distributions, Subgroup majorization., Shape optimal design criterion in linear models, A multivariate dispersion ordering based on quantiles more widely separated, Multivariate process capability via Löwner ordering

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