Estimation by the nearest neighbor rule under arbitrary sampling

S. E. Posner, S. R. Kulkarni

Research output: Chapter in Book/Report/Conference proceedingConference 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 Rr the convergence rate of the time-averaged risk is O(1/n2/r).

Original languageEnglish (US)
Title of host publicationProceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994
Number of pages1
DOIs
StatePublished - Dec 1 1994
Event1994 IEEE International Symposium on Information Theory, ISIT 1994 - Trondheim, Norway
Duration: Jun 27 1994Jul 1 1994

Publication series

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

Other

Other1994 IEEE International Symposium on Information Theory, ISIT 1994
CountryNorway
CityTrondheim
Period6/27/947/1/94

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Modeling and Simulation
  • Theoretical Computer Science
  • Information Systems

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