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2005.42: Neighbourhoods of independence and associated geometry

2005.42: Khadiga Arwini and CTJ Dodson (2005) Neighbourhoods of independence and associated geometry.

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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 2000 > 53 Differential geometry
MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2005.42
Deposited By:Prof CTJ Dodson
Deposited On:13 December 2005

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