### 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) |
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State | Published - Dec 1 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 |
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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

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## 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, .