The Annals of Statistics

Nearest neighbor classification with dependent training sequences

M. Holst and A. Irle

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Abstract

The asymptotic classification risk for nearest neighbor procedures is well understood in the case of i.i.d. training sequences. In this article, we generalize these results to a class of dependent models including hidden Markov models. In the case where the observed patterns have Lebesgue densities, the asymptotic risk takes the same expression as in the i.i.d. case. For discrete distributions, we show that the asymptotic risk depends on the rule used for breaking ties of equal distances.

Article information

Source
Ann. Statist. Volume 29, Number 5 (2001), 1424-1442.

Dates
First available in Project Euclid: 8 February 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1013203460

Digital Object Identifier
doi:10.1214/aos/1013203460

Mathematical Reviews number (MathSciNet)
MR1873337

Zentralblatt MATH identifier
1043.62057

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62G20: Asymptotic properties

Keywords
Nearest neighbor classification asymptotic risk dependent training samples

Citation

Holst, M.; Irle, A. Nearest neighbor classification with dependent training sequences. Ann. Statist. 29 (2001), no. 5, 1424--1442. doi:10.1214/aos/1013203460. https://projecteuclid.org/euclid.aos/1013203460.


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