The Annals of Mathematical Statistics

Nonparametric Discrimination Using Tolerance Regions

C. P. Quesenberry and M. P. Gessaman

Full-text: Open access

Abstract

A method is given which can be used to construct procedures for discriminating among distributions on a Euclidean space with continuous distribution functions. The decision space used includes "partial" decisions and the probabilities of errors are random variables with beta distributions. Emphasis is upon control of the distribution of the conditional overall probabilities of errors. These procedures can be used in a wide class of discrimination problems, such as, for example, discriminating among multivariate normal distributions with unknown, unequal dispersion matrices. A number of other writers have suggested nonparameteric discrimination procedures. The first work in this area, to the knowledge of these writers, was by Fix and Hodges [2]. Since the work by those authors has remained unpublished, a brief statement of its approach and results is given in Section 4 for comparison. Procedures have been suggested also by Stoller [3], Anderson [1] and Kendall [8].

Article information

Source
Ann. Math. Statist., Volume 39, Number 2 (1968), 664-673.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698425

Digital Object Identifier
doi:10.1214/aoms/1177698425

Mathematical Reviews number (MathSciNet)
MR228110

Zentralblatt MATH identifier
0162.22001

JSTOR
links.jstor.org

Citation

Quesenberry, C. P.; Gessaman, M. P. Nonparametric Discrimination Using Tolerance Regions. Ann. Math. Statist. 39 (1968), no. 2, 664--673. doi:10.1214/aoms/1177698425. https://projecteuclid.org/euclid.aoms/1177698425


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