A characterization of spherical distributions

It is shown that when the random vector X in Rn has a mean and when the conditional expectation E(u'Xv'X) = 0 for all vectors u, v [set membership, variant] Rn which satisfy u'v = 0, then the distribution of X is orthogonally invariant. A version of this characterization is also established when X does not have a mean vector.

MoreLess

Year of publication:	1986
Authors:	Eaton, Morris L.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 20.1986, 2, p. 272-276
Publisher:	Elsevier
Keywords:	orthogonally invariant distributions spherical distributions elliptical distribution characterization conditional expectation error distributions linear models

More details

Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005152834