Annals of Statistics

Asymptotically Efficient Solutions to the Classification Problem

Louis Gordon and Richard A. Olshen

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Abstract

We study a class of decision rules based on an adaptive partitioning of an Euclidean observation space. The class of partitions has a computationally attractive form, and the related decision rule is invariant under strictly monotone transformations of coordinate axes. We provide sufficient conditions that a sequence of decision rules be asymptotically Bayes risk efficient as sample size increases. The sufficient conditions involve no regularity assumptions on the underlying parent distributions.

Article information

Source
Ann. Statist., Volume 6, Number 3 (1978), 515-533.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344197

Digital Object Identifier
doi:10.1214/aos/1176344197

Mathematical Reviews number (MathSciNet)
MR468035

Zentralblatt MATH identifier
0437.62056

JSTOR
links.jstor.org

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62G20: Asymptotic properties 62P99: None of the above, but in this section

Keywords
Nonparametric discrimination nonparametric classification

Citation

Gordon, Louis; Olshen, Richard A. Asymptotically Efficient Solutions to the Classification Problem. Ann. Statist. 6 (1978), no. 3, 515--533. doi:10.1214/aos/1176344197. https://projecteuclid.org/euclid.aos/1176344197


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