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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 5, Fasc. 1,
pages 21 - 29
 

NON-ASYMPTOTIC MINIMAX RISK FOR HELLINGER BALLS

Lucien Birgé

Abstract: The following intuitively evident result is shown.

Given a probability P and a radius r , assume that we have to estimate an unknown law belonging to a sphere with centre P and radius r for the Hellinger distance using n 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 P of the sphere.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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