### Abstract

A binary classification problem is considered. The excess error probability of the k-nearest-neighbor classification rule according to the error probability of the Bayes decision is revisited by a decomposition of the excess error probability into approximation and estimation errors. Under a weak margin condition and under a modified Lipschitz condition or a local Lipschitz condition, tight upper bounds are presented such that one avoids the condition that the feature vector is bounded. The concept of modified Lipschitz condition is applied for discrete distributions, too. As a consequence of both concepts, we present the rate of convergence of L_{2} error for the corresponding nearest neighbor regression estimate.

Original language | English |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Journal of Machine Learning Research |

Volume | 18 |

Publication status | Published - Jun 1 2018 |

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### Keywords

- Classification
- Error probability
- K-nearest-neighbor rule
- Rate of convergence

### ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Statistics and Probability
- Artificial Intelligence

### Cite this

*Journal of Machine Learning Research*,

*18*, 1-16.