An equivalence criterion for infinite products of Cauchy measures

Autor:	Kazuki Okamura
Rok vydání:	2020
Předmět:	Statistics and Probability Pure mathematics Probability (math.PR) FOS: Mathematics Cauchy distribution Probability and statistics Infinite product Statistics Probability and Uncertainty Equivalence (measure theory) Mathematics - Probability 60G30 Mathematics
Zdroj:	Statistics & Probability Letters. 163:108797
ISSN:	0167-7152
Popis:	We give an equivalence-singularity criterion for infinite products of Cauchy measures under simultaneous shifts of the location and scale parameters. Our result is an extension of Lie and Sullivan's result giving an equivalence-singularity criterion under dilations of scale parameters. Our proof utilizes McCullagh's parameterization of the Cauchy distributions and maximal invariant, and a closed-form formula of the Kullback-Leibler divergence between two Cauchy measures given by Chyzak and Nielsen. Comment: 6 pages; Lemma 2.4 in the published version is wrong. It is corrected, and the proof is given
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5836b141c9714753950804624642dd10 https://doi.org/10.1016/j.spl.2020.108797 Zobrazit plný text záznamu Full Text from ScienceDirect