Sankhya: The Indian Journal of Statistics1993, Volume 55, Series A, Pt. 2, 214--225
ON A CLASS OF PROBABILITY DENSITY FUNCTIONS AND THEIR INFORMATION METRIC
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
This article in Mathematical Reviews.