Information geometry of small diffusions

Tomonari Sei; Fumiyasu Komaki

doi:10.1007/s11203-007-9011-2

Information geometry of small diffusions

Tomonari Sei, Fumiyasu Komaki

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	123-141
Number of pages	19
Journal	Statistical Inference for Stochastic Processes
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s11203-007-9011-2
Publication status	Published - 2008 Jun 1

Keywords

Curved exponential family
Information geometry
Second-order asymptotic efficiency
Small diffusion models

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s11203-007-9011-2

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AB - 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.

KW - Curved exponential family

KW - Information geometry

KW - Second-order asymptotic efficiency

KW - Small diffusion models

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JF - Statistical Inference for Stochastic Processes

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ER -

Information geometry of small diffusions

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Keywords

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