A note on Stein's lemma for multivariate elliptical distributions

Zinoviy Landsman, Steven Vanduffel, Jing Yao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2016-2022
Number of pages7
JournalJournal of Statistical Planning and Inference
Issue number11
Publication statusPublished - Nov 2013


  • Conditional expectation
  • Multivariate elliptical distribution
  • Siegel's formula
  • Stein's lemma

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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