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Dualistic Structure

In: Geometric Modeling in Probability and Statistics

Author

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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)

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.

Suggested Citation

  • Ovidiu Calin & Constantin Udrişte, 2014. "Dualistic Structure," Springer Books, in: Geometric Modeling in Probability and Statistics, edition 127, chapter 0, pages 223-255, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-07779-6_8
    DOI: 10.1007/978-3-319-07779-6_8
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