A Note on Stein's Lemma for Multivariate Elliptical Distributions

Abstract

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