NON-ASYMPTOTIC MINIMAX RISK FOR HELLINGER BALLS
Abstract: The following intuitively evident result is shown.
Given a probability and a radius , assume that we have to estimate an unknown law
belonging to a sphere with centre and radius for the Hellinger distance using
independent identically distributed observations. If the risk is measured by the square of the
Hellinger distance, then the observations carry no information and the best estimator is just
the centre of the sphere.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -