A distance between elliptical distributions based in an embedding into the Siegel group

Authors:
Miquel Calvo;Josep M. Oller
Affiliations:
Departament d'Estadistica, Facultat de Biologia, Diagonal 645, Universitat de Barcelona, 08028 Barcelona, Spain;Departament d'Estadistica, Facultat de Biologia, Diagonal 645, Universitat de Barcelona, 08028 Barcelona, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 2
Cited 2

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Geodesic estimation in elliptical distributions

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Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

International Journal of Computer Vision
On the Geometry of Multivariate Generalized Gaussian Models

Journal of Mathematical Imaging and Vision

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Abstract

This paper describes two different embeddings of the manifolds corresponding to many elliptical probability distributions with the informative geometry into the manifold of positive-definite matrices with the Siegel metric, generalizing a result published previously elsewhere. These new general embeddings are applicable to a wide class of elliptical probability distributions, in which the normal, t-Student and Cauchy are specific examples. A lower bound for the Rao distance is obtained, which is itself a distance, and, through these embeddings, a number of statistical tests of hypothesis are derived.