2005.42: Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions
2005.42: Khadiga Arwini and CTJ Dodson (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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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.
|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
|Deposited By:||Prof CTJ Dodson|
|Deposited On:||04 June 2007|
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