THE FISHER INFORMATION AND EXPONENTIAL FAMILIES
PARAMETRIZED BY A SEGMENT OF MEANS
Piotr Graczyk
Salha Mamane
Abstract: We consider natural and general exponential families on
parametrized by the means. We study the submodels 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 and . 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.