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An equivalence criterion for infinite products of Cauchy measures

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  • Okamura, Kazuki

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.

Suggested Citation

  • Okamura, Kazuki, 2020. "An equivalence criterion for infinite products of Cauchy measures," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220301000
    DOI: 10.1016/j.spl.2020.108797
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    Cited by:

    1. Yuichi Akaoka & Kazuki Okamura & Yoshiki Otobe, 2022. "Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 895-923, October.

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