The Annals of Statistics
- Ann. Statist.
- Volume 29, Number 5 (2001), 1424-1442.
Nearest neighbor classification with dependent training sequences
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.
Ann. Statist. Volume 29, Number 5 (2001), 1424-1442.
First available in Project Euclid: 8 February 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62G20: Asymptotic properties
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.