Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions

Arwini, Khadiga and Dodson, CTJ (2007) Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions. Central European Journal of Mathematics, 51. pp. 50-83. ISSN 1644-3616

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Abstract

We provide explicit information geometric tubular neighbourhoods containing all bivariate processes sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the alpha-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate processes; the topological character of the results makes them stable under small perturbations, which is important for applications.

Item Type:	Article
Uncontrolled Keywords:	information geometry, statistical manifold, neighbourhoods of independence, exponential distribution, Freund distribution, Gaussian distribution
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User:	Prof CTJ Dodson
Date Deposited:	04 Jun 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/816

Available Versions of this Item

• Neighbourhoods of independence and associated geometry. (deposited 13 Dec 2005)
  • Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions. (deposited 04 Jun 2007) [Currently Displayed]

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