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Chapitre D'ouvrage Année : 2023

The Fisher-Rao geometry of CES distributions

Résumé

When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as the Fisher-Rao information geometry. Interestingly, this yields a point of view that allows for leveragingmany tools from differential geometry. After a brief introduction about these concepts, we will present some practical uses of these geometric tools in the framework of elliptical distributions. This second part of the exposition is divided into three main axes: Riemannian optimization for covariance matrix estimation, Intrinsic Cram\'er-Rao bounds, and classification using Riemannian distances.
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Dates et versions

hal-04225646 , version 1 (03-10-2023)

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Florent Bouchard, Arnaud Breloy, Antoine Collas, Alexandre Renaux, Guillaume Ginolhac. The Fisher-Rao geometry of CES distributions. Springer. Elliptical Distributions in Signal Processing, In press. ⟨hal-04225646⟩
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