Bernoulli

  • 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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Abstract

Let be a measure space, and let denote the set of the -almost surely strictly positive probability densities. It was shown by Pistone and Sempi in 1995 that the global geometry on can be realized by an affine atlas whose charts are defined locally by the mappings , where is a suitable open set containing , is the Kullback--Leibler relative information and is the vector space of centred and exponentially -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.

Article information

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

Dates
First available in Project Euclid: 19 February 2007

Permanent link to this document
http://projecteuclid.org/euclid.bj/1171899326

Mathematical Reviews number (MathSciNet)
MR1704564

Zentralblatt MATH identifier
0947.62003

Keywords
exponential families exponential statistical manifolds information mean parameters Orlicz spaces orthogonality

Citation

Pistone, Giovanni; Piera Rogantin, Maria. The exponential statistical manifold: mean parameters, orthogonality and space transformations. Bernoulli 5 (1999), no. 4, 721--760. http://projecteuclid.org/euclid.bj/1171899326.


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