The Fisher information and exponential families parametrized by a segment of means

  1. Piotr Graczyk
  2. Salha Mamane

Abstract

We consider natural and general exponential families (Qm)m∈M on ℜd parametrized by the means. We study the submodels (Qθm1+(1−θ)m2 )∈[0;1] parametrized by a segment in the means domain from the point of view of the Fisher information. Such a parametrization allows for a parsimonious model and is particularly useful in practical situations when hesitating between two parameters m1 and m2. The most interesting cases are multivariate Gaussian and Wishart models with matrix parameters.

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Probability and Mathematical Statistics

35, z. 1, 2015

Pages from 73 to 90

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