An equivalence criterion for infinite products of Cauchy measures
arXiv:2004.06442 · doi:10.1016/j.spl.2020.108797
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.
6 pages; Lemma 2.4 in the published version is wrong. It is corrected, and the proof is given