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Information geometry of small diffusions

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Abstract

Information geometrical quantities such as metric tensors and connection coefficients for small diffusion models are obtained. Asymptotic properties of bias-corrected estimators for small diffusion models are investigated from the viewpoint of information geometry. Several results analogous to those for independent and identically distributed (i.i.d.) models are obtained by using the asymptotic normality of the statistics appearing in asymptotic expansions. In contrast to the asymptotic theory for i.i.d.models, the geometrical quantities depend on the magnitude of noise.

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Abbreviations

i.i.d.:

independent and identically distributed

MLE:

maximum likelihood estimator

EPE:

e-projection estimator

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Tomonari Sei & Fumiyasu Komaki

Authors
  1. Tomonari Sei
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  2. Fumiyasu Komaki
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Correspondence to Tomonari Sei.

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Sei, T., Komaki, F. Information geometry of small diffusions. Stat Infer Stoch Process 11, 123–141 (2008). https://doi.org/10.1007/s11203-007-9011-2

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  • DOI: https://doi.org/10.1007/s11203-007-9011-2

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