The Hilbert Riemannian structure of equivalent Gaussian measures associated with the Fisher information
type: Item
instance of: scholarly article
title: The Hilbert Riemannian structure of equivalent Gaussian measures associated with the Fisher information
zbMATH Open document ID: 0829.60034
author: Jun Sekine
published in: Osaka Journal of Mathematics
publication date: 1996-01-15T00:00:00Z
review text: Rao has firstly introduced the Riemannian structure associated with the Fisher information matrix over a finite-dimensional parametrized statistical model. He proposed the Riemannian distance as a measure of dissimilarity between two probability measures [cf., for example, \textit{S.-I. Amari}, \textit{O. E. Barndorff-Nielsen}, \textit{R. E. Kass}, \textit{S. L. Lauritzen} and \textit{C. R. Rao}, ``Differential geometry in statistical inference'' (1987; Zbl 0694.62001)]. \textit{S.-I. Amari} [``Differential- geometrical methods in statistics'' (1985; Zbl 0559.62001)] introduced a pair of dual affine connections with respect to the metric and discussed the differential geometry of the space of a finite-dimensional parametrized statistical model. It provides a differential geometrical meaning to statistical inference. In the present paper, we realize the above idea for a family of equivalent (i.e., mutually absolute continuous) Gaussian measures on a Banach space.
Mathematics Subject Classification ID: 60G30
zbMATH DE Number: 755437
zbMATH Keywords: Fisher information matrix
zbMATH Keywords: statistical model
zbMATH Keywords: differential geometry
zbMATH Keywords: Gaussian measures on a Banach space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 755437