An equivalence criterion for infinite products of Cauchy measures

Kazuki Okamura

Statistics & Probability Letters, 2020, vol. 163, issue C

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 parametrization 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: Cauchy distribution; Equivalence of measures; Kakutani dichotomy (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2020.108797

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