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

Graczyk P., Mamane S.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 1

73--90

We consider natural and general exponential families (Qm)mϵM on Rd parametrized by the means. We study the submodels (Q0m1+(1−0)m2)0ϵ[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.