The paper is concerned with the geometrical structures induced by the Fisher information metric in statistical models with location parameters. Simple and practical criteria for level submanifolds to be geodesic submanifolds of the Riemannian manifold determined by the above metric, are established. These criteria are of practical use in constructing statistical tests based on the information geodesic distance of the statistical model, and they can be easily implemented on any symbolic computation program such as reduce of mathematica. © 1992.
- Fisher information matrix: Information distance: Rao distance: Geodesic submanifold: Location parameter: Statistical model: Riemannian manifold: Informative geometry: Elliptic model.