Estimation by the nearest neighbor rule under arbitrary sampling

S. E. Posner; S. R. Kulkarni

doi:10.1109/ISIT.1994.394930

Estimation by the nearest neighbor rule under arbitrary sampling

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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)
Title of host publication	Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	41
Number of pages	1
ISBN (Print)	0780320158, 9780780320154
DOIs	https://doi.org/10.1109/ISIT.1994.394930
State	Published - 1994
Event	1994 IEEE International Symposium on Information Theory, ISIT 1994 - Trondheim, Norway Duration: Jun 27 1994 → Jul 1 1994

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Other

Other	1994 IEEE International Symposium on Information Theory, ISIT 1994
Country/Territory	Norway
City	Trondheim
Period	6/27/94 → 7/1/94

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Applied Mathematics
Modeling and Simulation

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10.1109/ISIT.1994.394930

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Posner, S. E., & Kulkarni, S. R. (1994). Estimation by the nearest neighbor rule under arbitrary sampling. In Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994 (pp. 41). Article 394930 (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.1994.394930

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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",

doi = "10.1109/ISIT.1994.394930",

language = "English (US)",

isbn = "0780320158",

series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "41",

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address = "United States",

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

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Posner, SE & Kulkarni, SR 1994, Estimation by the nearest neighbor rule under arbitrary sampling. in Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994., 394930, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 41, 1994 IEEE International Symposium on Information Theory, ISIT 1994, Trondheim, Norway, 6/27/94. https://doi.org/10.1109/ISIT.1994.394930

Estimation by the nearest neighbor rule under arbitrary sampling. / Posner, S. E.; Kulkarni, S. R.
Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994. Institute of Electrical and Electronics Engineers Inc., 1994. p. 41 394930 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

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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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PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 1994 IEEE International Symposium on Information Theory, ISIT 1994

Y2 - 27 June 1994 through 1 July 1994

ER -

Estimation by the nearest neighbor rule under arbitrary sampling

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