Neighbourhoods of independence and associated geometry

Arwini, Khadiga and Dodson, CTJ (2005) Neighbourhoods of independence and associated geometry. [MIMS Preprint]

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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: MIMS Preprint
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: 13 Dec 2005
Last Modified: 08 Nov 2017 18:18

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