Published in The Annals of Probability, Volume 17, Issue 3, September 1, 1989, pages 1325-1334. Copyright © 1989 Institute of Mathematical Statistics. The definitive version is available at http://dx.doi.org/10.1214/aos/1176347272.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
Optimal-partitioning and minimax risk inequalities are obtained for the classification and multi-hypotheses testing problems. Best possible bounds are derived for the minimax risk for location parameter families, based on the tail concentrations and Levy concentrations of the distributions. Special attention is given to continuous distributions with the maximum likelihood ratio property and to symmetric unimodal continuous distributions. Bounds for general (including discontinuous) distributions are also obtained.