The Annals of Statistics
- Ann. Statist.
- Volume 17, Number 3 (1989), 1325-1334.
Optimal-Partitioning Inequalities in Classification and Multi-Hypotheses Testing
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.
Ann. Statist., Volume 17, Number 3 (1989), 1325-1334.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 28B05: Vector-valued set functions, measures and integrals [See also 46G10]
Hill, Theodore P.; Tong, Y. L. Optimal-Partitioning Inequalities in Classification and Multi-Hypotheses Testing. Ann. Statist. 17 (1989), no. 3, 1325--1334. doi:10.1214/aos/1176347272. https://projecteuclid.org/euclid.aos/1176347272