### 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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Title of host publication | Challenges in Computational Statistics and Data Mining |

Publisher | Springer International Publishing |

Pages | 71-91 |

Number of pages | 21 |

Volume | 605 |

ISBN (Print) | 9783319187815, 9783319187808 |

DOIs | |

Publication status | Published - Jul 7 2015 |

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### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)

### Cite this

*Challenges in Computational Statistics and Data Mining*(Vol. 605, pp. 71-91). Springer International Publishing. https://doi.org/10.1007/978-3-319-18781-5_5