Contrast Functions Geometry

Ovidiu Calin and Constantin Udrişte
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Ovidiu Calin: Eastern Michigan University, Department of Mathematics
Constantin Udrişte: University Politehnica of Bucharest, Faculty of Applied Sciences Department of Mathematics-Informatics

Chapter Chapter 11 in Geometric Modeling in Probability and Statistics, 2014, pp 303-320 from Springer

Abstract: Abstract Contrast functions, called also divergence functions, are distance-like quantities which measure the asymmetric “proximity” of two probability density functions on a statistical manifold or statistical model 𝒮 $$\mathcal{S}$$ . A contrast function, D(p | | q), for density functions p , q ∈ 𝒮 $$p,q \in \mathcal{S}$$ , is a smooth, non-negative function that vanishes for p = q. Eguchi [38, 39, 41] has shown that a contrast function D induces a Riemannian metric by its second order derivatives, and a pair of dual connections by its third order derivatives.

Keywords: Convex Function; Canonical Divergence; Coordinate Chart; Contrast Function; Dualistic Structure (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-07779-6_11

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