A Note on Stein's Lemma for Multivariate Elliptical Distributions

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