A Note on Stein's Lemma for Multivariate Elliptical Distributions
Journal of Statistical Planning and Inference, Forthcoming
11 Pages Posted: 3 Jun 2013 Last revised: 6 Nov 2014
Date Written: May 26, 2013
When two random variables are bivariate normally distributed Stein's original lemma allows to conveniently express the covariance of the first variable with a function of the second. Landsman & Neslehova (2007) extend this seminal result to the family of multivariate elliptical distributions. In this paper we use the technique of conditioning to provide a more elegant proof for their result. In doing so we also present a new proof for the classical linear regression result that holds for the elliptical family.
Keywords: Conditional distribution, Covariance, Regression
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