Covariance identities for normal variables via convex polytopes
The main result is an extension of a covariance identity involving correlated Gaussian random variables which is due to \textit{A. F. Siegel} [J. Am. Stat. Assoc. 88, No. 421, 77-80 (1993; Zbl 0772.62028)]. The obtained generalization of this identity reveals an interesting (rather unexpected) connection with basic notions and relationships from convex geometry such as support function and the Euler-Schlaefli functional for the Steiner point of a convex body.
scientific article; zbMATH DE number 1031773