Stein's Lemma for elliptical random vectors

Zinoviy Landsman; Johanna Nešlehová

doi:10.1016/j.jmva.2007.05.006

Stein's Lemma for elliptical random vectors

Zinoviy Landsman, Johanna Nešlehová

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

Original language	English
Pages (from-to)	912-927
Number of pages	16
Journal	Journal of Multivariate Analysis
Volume	99
Issue number	5
DOIs	https://doi.org/10.1016/j.jmva.2007.05.006
State	Published - May 2008

Bibliographical note

Funding Information:
The first author acknowledges financial support by the FIM, ETH Zurich. The second author was supported by RiskLab, ETH Zurich. The authors thank Paul Embrechts for bringing Froot [8] to their attention and for fruitful discussions. They are grateful to the referees for their thorough comments and suggestions.

Keywords

Density generator
Elliptical distribution
Generalized hyperbolic distribution
Normal distribution
Normal mixtures
Pearson Type VII distribution
Spherical distribution
Stein's Lemma
Student t distribution

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2007.05.006

Cite this

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title = "Stein's Lemma for elliptical random vectors",

abstract = "For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.",

keywords = "Density generator, Elliptical distribution, Generalized hyperbolic distribution, Normal distribution, Normal mixtures, Pearson Type VII distribution, Spherical distribution, Stein's Lemma, Student t distribution",

author = "Zinoviy Landsman and Johanna Ne{\v s}lehov{\'a}",

note = "Funding Information: The first author acknowledges financial support by the FIM, ETH Zurich. The second author was supported by RiskLab, ETH Zurich. The authors thank Paul Embrechts for bringing Froot [8] to their attention and for fruitful discussions. They are grateful to the referees for their thorough comments and suggestions.",

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N2 - For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

AB - For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

KW - Density generator

KW - Elliptical distribution

KW - Generalized hyperbolic distribution

KW - Normal distribution

KW - Normal mixtures

KW - Pearson Type VII distribution

KW - Spherical distribution

KW - Stein's Lemma

KW - Student t distribution

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SP - 912

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

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ER -

Stein's Lemma for elliptical random vectors

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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