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

Zinoviy Landsman

University of Haifa, Department of Statistics

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Jing Yao

Vrije Universiteit Brussel (VUB)

Date Written: May 26, 2013

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

Suggested Citation

Landsman, Zinoviy and Vanduffel, Steven and Yao, Jing, A Note on Stein's Lemma for Multivariate Elliptical Distributions (May 26, 2013). Journal of Statistical Planning and Inference, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2272981

Zinoviy Landsman

University of Haifa, Department of Statistics ( email )

Haifa, 31905
Israel
+972-4-8249003 (Phone)

HOME PAGE: http://stat.haifa.ac.il/~landsman

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

Jing Yao (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, B-1050
Belgium

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