On Rao distance asymptotic distribution

Abstract

This paper is concerned with the study of the asymptotic properties of Rao distance maximum-likelihood estimation obtained from two independent samples of two statistical populations, under certain regularity conditions. These results allow the construction, by meaos of the Rao distance, of a statistical test to compare different populations, which may be regarded as an alternative to the standard likelihood ratio test. Furthermore, a geometrical model is supplied which can be used to obtain graphical outputs through numerical taxonomy methods or multidimensional scaling techniques. Finally, sorne of the previously-mentioned methods are illustrated by meaos of a specific example based on the univariate normal distribution.