A characterization of spherical distributions

Morris L. Eaton

Journal of Multivariate Analysis, 1986, vol. 20, issue 2, 272-276

Abstract: 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.

Keywords: orthogonally; invariant; distributions; spherical; distributions; elliptical; distribution; characterization; conditional; expectation; error; distributions; linear; models (search for similar items in EconPapers)
Date: 1986
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Citations: View citations in EconPapers (24)

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