On the property of multivariate generalized hyperbolic distribution and the Stein-type inequality

Xiang Deng, Jing Yao

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This note consists of two parts. In the first part, we provide a pedagogic review on the multivariate generalized hyperbolic (MGH) distribution. We show that this probability family is close under margining, conditioning, and linear transforms; however, such property does not hold for its subclasses. In the second part, we obtain the Stein-type inequality in the context of MGH distribution. Moreover, we apply the Stein-type inequality to prove a lower bound for Var[h(X)]. Particularly, we present examples when X belongs to some well-known subclasses in MGH family.

Original languageEnglish
Pages (from-to)5346-5356
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Volume47
Issue number21
Early online date12 Oct 2018
DOIs
Publication statusPublished - 2 Nov 2018

Keywords

  • Bounds for Var[h(X)]
  • multivariate generalized hyperbolic distribution
  • Stein-type inequality
  • Stein’s lemma

ASJC Scopus subject areas

  • Statistics and Probability

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