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A note on Stein's lemma for multivariate elliptical distributions

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Volume
143
Issue
11
Identifiers
DOI: 10.1016/j.jspi.2013.06.003
Keywords
  • Conditional Expectation
  • Stein'S Lemma
  • Multivariate Elliptical Distribution
  • Siegel'S Formula

Abstract

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 and Neslehova (2008) 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.

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