• Bernoulli
  • Volume 5, Number 4 (1999), 721-760.

The exponential statistical manifold: mean parameters, orthogonality and space transformations

Giovanni Pistone and Maria Piera Rogantin

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Let ( X,cal X,μ) be a measure space, and let cal M (X,cal X,μ) denote the set of the μ -almost surely strictly positive probability densities. It was shown by Pistone and Sempi in 1995 that the global geometry on cal M (X,cal X,μ) can be realized by an affine atlas whose charts are defined locally by the mappings cal M (X,cal X,μ)cal U pqlog(q/p)+K(p,q)B p , where cal U p is a suitable open set containing p , K (p,q) is the Kullback--Leibler relative information and B p is the vector space of centred and exponentially ( pμ) -integrable random variables. In the present paper we study the transformation of such an atlas and the related manifold structure under basic transformations, i.e. measurable transformation of the sample space. A generalization of the mixed parametrization method for exponential models is also presented.

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Bernoulli, Volume 5, Number 4 (1999), 721-760.

First available in Project Euclid: 19 February 2007

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exponential families exponential statistical manifolds information mean parameters Orlicz spaces orthogonality


Pistone, Giovanni; Piera Rogantin, Maria. The exponential statistical manifold: mean parameters, orthogonality and space transformations. Bernoulli 5 (1999), no. 4, 721--760.

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