On the Conditional Variance for Scale Mixtures of Normal Distributions

✍ Scribed by Stamatis Cambanis; Stergios B Fotopoulos; Lijian He

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 210 KB
• Volume: 74
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1999.1888

✦ Synopsis

For a scale mixture of normal vector, X=A 1Â2 G, where X, G # R n and A is a positive variable, independent of the normal vector G, we obtain that the conditional variance covariance, Cov(X 2 | X 1 ), is always finite a.s. for m 2, where X 1 # R n and m<n, and remains a.s. finite even for m=1, if and only if the square root moment of the scale factor is finite. It is shown that the variance is not degenerate as in the Gaussian case, but depends upon a function S A, m ( } ) for which various properties are derived. Application to a uniform and stable scale of normal distributions are also given.