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

Xiang Deng and Jing Yao

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 21, 5346-5356

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.

Date: 2018
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DOI: 10.1080/03610926.2017.1390134

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