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

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.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