Estimation by the nearest neighbor rule under arbitrary sampling

S. E. Posner, S. R. Kulkarni

Research output: Contribution to conferencePaper

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)
StatePublished - Dec 1 1994
EventProceedings of the 1994 IEEE International Symposium on Information Theory - Trodheim, Norw
Duration: Jun 27 1994Jul 1 1994

Other

OtherProceedings of the 1994 IEEE International Symposium on Information Theory
CityTrodheim, Norw
Period6/27/947/1/94

All Science Journal Classification (ASJC) codes

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

Fingerprint Dive into the research topics of 'Estimation by the nearest neighbor rule under arbitrary sampling'. Together they form a unique fingerprint.

  • Cite this

    Posner, S. E., & Kulkarni, S. R. (1994). Estimation by the nearest neighbor rule under arbitrary sampling. Paper presented at Proceedings of the 1994 IEEE International Symposium on Information Theory, Trodheim, Norw, .