### Abstract

A binary classification problem is considered, where the posteriori probability is estimated by the nonparametric kernel regression estimate with naive kernel. The excess error probability of the corresponding plug-in decision classification rule according to the error probability of the Bayes decision is studied such that the excess error probability is decomposed into approximation and estimation error. A general formula is derived for the approximation error. Under a weak margin condition and various smoothness conditions, tight upper bounds are presented on the approximation error. By a Berry-Esseen type central limit theorem a general expression for the estimation error is shown.

Original language | English |
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Pages (from-to) | 71-91 |

Number of pages | 21 |

Journal | Studies in Computational Intelligence |

Volume | 605 |

DOIs | |

Publication status | Published - Jan 1 2016 |

### Keywords

- Classification error probability
- Kernel rule
- Lower bound
- Margin condition
- Upper bound

### ASJC Scopus subject areas

- Artificial Intelligence

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## Cite this

*Studies in Computational Intelligence*,

*605*, 71-91. https://doi.org/10.1007/978-3-319-18781-5_5