Estimation by the nearest neighbor rule under arbitrary sampling

S. E. Posner; S. R. Kulkarni

Estimation by the nearest neighbor rule under arbitrary sampling

Research output: Contribution to conference › Paper › peer-review

Abstract

We introduce a new estimation problem in which the samples can be chosen arbitrarily. We show that for every sequence of samples the asymptotic time-average of nearest neighbor risks equals twice the time-average of the conditional Bayes risks of the sequence. Rates of convergence for nearest neighbor estimation are established in terms of metric covering numbers of the underlying space. In particular, for compact subsets of R^r the convergence rate of the time-averaged risk is O(1/n^2/r).

Original language	English (US)
State	Published - 1994
Event	Proceedings of the 1994 IEEE International Symposium on Information Theory - Trodheim, Norw Duration: Jun 27 1994 → Jul 1 1994

Other

Other	Proceedings of the 1994 IEEE International Symposium on Information Theory
City	Trodheim, Norw
Period	6/27/94 → 7/1/94

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Cite this

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title = "Estimation by the nearest neighbor rule under arbitrary sampling",

abstract = "We introduce a new estimation problem in which the samples can be chosen arbitrarily. We show that for every sequence of samples the asymptotic time-average of nearest neighbor risks equals twice the time-average of the conditional Bayes risks of the sequence. Rates of convergence for nearest neighbor estimation are established in terms of metric covering numbers of the underlying space. In particular, for compact subsets of Rr the convergence rate of the time-averaged risk is O(1/n2/r).",

author = "Posner, {S. E.} and Kulkarni, {S. R.}",

year = "1994",

language = "English (US)",

note = "Proceedings of the 1994 IEEE International Symposium on Information Theory ; Conference date: 27-06-1994 Through 01-07-1994",

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T1 - Estimation by the nearest neighbor rule under arbitrary sampling

AU - Posner, S. E.

AU - Kulkarni, S. R.

PY - 1994

Y1 - 1994

N2 - We introduce a new estimation problem in which the samples can be chosen arbitrarily. We show that for every sequence of samples the asymptotic time-average of nearest neighbor risks equals twice the time-average of the conditional Bayes risks of the sequence. Rates of convergence for nearest neighbor estimation are established in terms of metric covering numbers of the underlying space. In particular, for compact subsets of Rr the convergence rate of the time-averaged risk is O(1/n2/r).

AB - We introduce a new estimation problem in which the samples can be chosen arbitrarily. We show that for every sequence of samples the asymptotic time-average of nearest neighbor risks equals twice the time-average of the conditional Bayes risks of the sequence. Rates of convergence for nearest neighbor estimation are established in terms of metric covering numbers of the underlying space. In particular, for compact subsets of Rr the convergence rate of the time-averaged risk is O(1/n2/r).

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UR - http://www.scopus.com/inward/citedby.url?scp=0028699215&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:0028699215

T2 - Proceedings of the 1994 IEEE International Symposium on Information Theory

Y2 - 27 June 1994 through 1 July 1994

ER -

Estimation by the nearest neighbor rule under arbitrary sampling

Abstract

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All Science Journal Classification (ASJC) codes

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