Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 214--225

ON A CLASS OF PROBABILITY DENSITY FUNCTIONS AND THEIR INFORMATION METRIC

By

ANTONIO MIÑARRO

And

JOSEP M. OLLER, University of Barcelona 

SUMMARY. We introduce a class of probability density functions based on a Hilbert space representation of probability measures. Functions obtained may be characterised in a finite dimensional parametric manifold and the informative geometry of the model has been studied. Manifolds are of positive constant Reimannian curvature and the expression for the geodesics and for the Rao distance between two distributions has also been obtained. An example is introduced and studied from a probabilistic point of view, and finally we introduce a stepwise algorithm for nonparametric density estimation based on likelihood increments

.

AMS (1980) subject classification. 62G05,62E15, 62A99

Key words and phrases. Informative geometry, nonparametric density estimation

FULL PAPER.

This article in Mathematical Reviews.