The Annals of Statistics

Optimal-Partitioning Inequalities in Classification and Multi-Hypotheses Testing

Theodore P. Hill and Y. L. Tong

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Abstract

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.

Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1325-1334.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347272

Digital Object Identifier
doi:10.1214/aos/1176347272

Mathematical Reviews number (MathSciNet)
MR1015154

Zentralblatt MATH identifier
0683.62036

JSTOR
links.jstor.org

Subjects
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]

Keywords
Optimal-partitioning inequalities minimax risk classification and discriminant analysis multi-hypotheses testing convexity theorem concentration function tail concentration

Citation

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


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