Dualistic Structure

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 8 in Geometric Modeling in Probability and Statistics, 2014, pp 223-255 from Springer

Abstract: Abstract Statistical manifolds are abstract generalizations of statistical models. Even if a statistical manifold is treated as a purely geometric object, however, the motivation for the definitions is inspired from statistical models. In this new framework, the manifold of density functions is replaced by an arbitrary Riemannian manifold M, and the Fisher information matrix is replaced by the Riemannian metric g of the manifold M. The dual connections ∇(−1) and ∇(1) are replaced by a pair of dual connections ∇ and ∇∗. The skewness tensor, which measures the cummulants of the third order on a statistical model, is replaced by a 3-covariant skewness tensor.

Keywords: Skewness Tensor; Dual Connection; Statistical Manifold; Arbitrary Riemannian Manifold; Relative Curvature Tensor (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-07779-6_8

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