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Limiting behavior of relative Rényi entropy in a non-regular location shift family

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Abstract

We calculate the limiting behavior of relative Rényi entropy between adjacent two probability distribution in a non-regular location-shift family which is generated by a probability distribution whose support is an interval or a half-line. This limit can be regarded as a generalization of Fisher information, and seems closely related to information geometry and large deviation theory.

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Authors and Affiliations

  1. ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency (JST), Tokyo, 113-0033, Japan

    Masahito Hayashi

  2. Superrobust Computation Project, Information Science and Technology Strategic Core (21st Century COE by MEXT), Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Masahito Hayashi

  3. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8579, Japan

    Masahito Hayashi

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  1. Masahito Hayashi
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Correspondence to Masahito Hayashi.

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Hayashi, M. Limiting behavior of relative Rényi entropy in a non-regular location shift family. Ann Inst Stat Math 62, 547–569 (2010). https://doi.org/10.1007/s10463-008-0182-4

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  • DOI: https://doi.org/10.1007/s10463-008-0182-4

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