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Convex polytopes and Gaussian covariances

Published online by Cambridge University Press:  01 July 2016

R. A. Vitale
R. A. Vitale*
Affiliation:
University of Connecticut
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Extract

Siegel (1993) presented a covariance identity involving normal variables that seems to flout notions of dependence. We show that it has an explanation from an unexpected quarter: convex geometry and the centroid known as the Steiner point. In the same geometric spirit, we introduce another identity for Gaussian covariances based on an Euler identity for the Steiner point.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 343
Copyright
Copyright © Applied Probability Trust 1996 

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References

Siegel, A. F. (1993) A surprising covariance involving the minimum of multivariate normal variables. J. Amer. Statist. Assoc. 88, 77–80.Google Scholar