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A Characterization and a Variational Inequality for the Multivariate Normal Distribution

Part of: Multivariate analysis

Published online by Cambridge University Press:  09 April 2009

Wolfgang Stadje
Wolfgang Stadje
Affiliation:
Fachbereich Mathematik Universitat OsnabriickAlbrechtstrasse 28 West, Germany
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Various generalizations of the Maxwell characterization of the multivariate standard normal distribution are derived. For example the following is proved: If for a k-dimensional random vector X there exists an n ∈ {l, …, k − l} such that for each n-dimensional linear subspace H Rk the projections of X on H and H⊥ are independent, X is normal. If X has a rotationally symmetric density and its projection on some H has a density of the same functional form, X is normal. Finally we give a variational inequality for the multivariate normal distribution which resembles the isoperimetric inequality for the surface measure on the sphere.

MSC classification

Secondary: 62H05: Characterization and structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 3 , December 1987 , pp. 366 - 374
Copyright
Copyright © Australian Mathematical Society 1987

References

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