Optimal-Partitioning Inequalities in Classification and Multi-Hypotheses Testing
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.
Theodore P. Hill and Y. L. Tong. "Optimal-Partitioning Inequalities in Classification and Multi-Hypotheses Testing" The Annals of Probability 17.3 (1989): 1325-1334.
Available at: http://works.bepress.com/tphill/2