On Representations of Divergence Measures and Related Quantities in Exponential Families

Autor:	Stefan Bedbur, Udo Kamps
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	exponential family cumulant function mean value function divergence measure distance measure affinity Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 23, Iss 6, p 726 (2021)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e23060726
Popis:	Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback–Leibler divergence, the Cressie–Read divergence, the Rényi divergence, and the Hellinger metric, can be explicitly expressed in terms of the respective cumulant function and mean value function. Moreover, the same applies to related entropy and affinity measures. We compile representations scattered in the literature and present a unified approach to the derivation in exponential families. As a statistical application, we highlight their use in the construction of confidence regions in a multi-sample setup.
Databáze:	Directory of Open Access Journals
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