Some remarks on the individuals-score distance and its applications to statistical inference

Abstract

This paper is concerned with the study of some properties of the distance between statistical individuals based on representations on the dual tangent space of a parametric manifold representation of a statistical model. Explicit expressions for distances are obtained for well-known families of distributions. We have also considered applications of the distance to parameter estimation, testing statistical hypotheses and discriminant analysis.

AMS 1980 subjects classifications: 62A99, 62F03, 62F10.

Keywords and phrases:informative geometry, statistical individuals, distances between individuals, statistical inference.