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arXiv · 2004.06442

An equivalence criterion for infinite products of Cauchy measures

Kazuki Okamura
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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.

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Kazuki Okamura. 2020-04-14. An equivalence criterion for infinite products of Cauchy measures. https://doi.org/10.1016/j.spl.2020.108797

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