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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 35, Fasc. 1,
pages 73 - 90
 

THE FISHER INFORMATION AND EXPONENTIAL FAMILIES PARAMETRIZED BY A SEGMENT OF MEANS

Piotr Graczyk
Salha Mamane

Abstract: We consider natural and general exponential families (Q  )
  m m∈M  on ℝd  parametrized by the means. We study the submodels (Q           )
  θm1+(1-θ)m2 θ∈[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 m
 1  and m
 2  . The most interesting cases are multivariate Gaussian and Wishart models with matrix parameters.

2000 AMS Mathematics Subject Classification: Primary: 62H12; Secondary: 62H10.

Keywords and phrases: Fisher information, efficient estimator, exponential family, multivariate Gaussian distribution, Wishart distribution, parsimony.

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