The Fisher information and exponential families parametrized by a segment of means
Słowa kluczowe:Fisher information, efficient estimator, exponential family, multivariate Gaussian distribution, Wishart distribution, parsimony
We consider natural and general exponential families Qmm∈M on ℜd parametrized by the means. We study the submodels Qθm1+1−θm2 ∈[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.