1992
DOI: 10.32917/hmj/1206128508
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Geometry of minimum contrast

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Cited by 99 publications
(95 citation statements)
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“…(2.4) Therefore, D (α) as parameterized by α ∈ R, for a fixed , properly form a family of divergence functions (also known as deviations or contrast functions) in the sense of Eguchi (1983Eguchi ( , 1992, Amari (1982Amari ( , 1985, Kaas & Vos (1997), and Amari & Nagaoka (2000).…”
Section: Convexity and Divergence Functionsmentioning
confidence: 98%
See 1 more Smart Citation
“…(2.4) Therefore, D (α) as parameterized by α ∈ R, for a fixed , properly form a family of divergence functions (also known as deviations or contrast functions) in the sense of Eguchi (1983Eguchi ( , 1992, Amari (1982Amari ( , 1985, Kaas & Vos (1997), and Amari & Nagaoka (2000).…”
Section: Convexity and Divergence Functionsmentioning
confidence: 98%
“…Divergence function or functional 1 is an essential subject in information geometry, the differential geometric study of the manifold of (parametric or nonparametric) probability distributions (Amari, 1982(Amari, , 1985Eguchi, 1983Eguchi, , 1992Amari & Nagaoka, 2000). As first demonstrated by Eguchi (1983), a well-defined divergence function (also called a contrast function) with vanishing first order (in the vicinity of p = q) term will induce a Riemannian metric g by its second-order properties and a pair of dual (also called conjugate) connections ( , * ) by its third-order properties, where the dual connections jointly preserve the metric under parallel transport.…”
Section: Introductionmentioning
confidence: 98%
“…Then the restriction associates with a Riemannian metric g ( ) , a pair of linear connections ( ) and * ( ) on the differentiable manifold M, cf. [6]. In fact the Riemannian metric is given by…”
Section: Asymmetry Of D In Information Geometrymentioning
confidence: 98%
“…[5,6]. We assume the differentiability of over M × M restricted from P × P writing ( 1 , 2 ) = (f (·, 1 ), f (·, 2 )).…”
Section: Asymmetry Of D In Information Geometrymentioning
confidence: 99%
“…In particular, the triplets (M, ∇, h) and (M, ∇ * , h) form mutually dual statistical manifolds (see [2] and [6]). Since a contrast function ρ is asymmetric in general, ρ induces a dualistic geometric structure on M. The second order derivatives give a semi-Riemannian metric h, and the third order derivatives give a pair of torsion-free affine connections ∇ and ∇ * .…”
Section: Introductionmentioning
confidence: 99%