An equivalence criterion for infinite products of Cauchy measures
Probability
2021-01-21 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2004.06442,
title = {An equivalence criterion for infinite products of Cauchy measures},
author = {Kazuki Okamura},
journal= {arXiv preprint arXiv:2004.06442},
year = {2021}
}
Comments
6 pages; Lemma 2.4 in the published version is wrong. It is corrected, and the proof is given