### Abstract

AIC-type information criterion is generally estimated by the bias-corrected maximum log-likelihood. In regular models, the bias can be estimated by p, where p is the number of parameters. The present paper considers the AIC-type information criterion for change-point models which are not regular, the bias of which will not be the same as for regular models. The bias is shown to depend on the expected maximum of a random walk with negative drift. Furthermore, it is shown that by using an approximation to a Brownian motion, the evaluated bias is given by 3m + p_{m} (not m + p_{m}), where m is the number of change-points and p_{m} is the number of regular parameters, which differs from regular models.

Original language | English |
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Pages (from-to) | 237-247 |

Number of pages | 11 |

Journal | Statistics and Probability Letters |

Volume | 72 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 1 2005 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

*Statistics and Probability Letters*,

*72*(3), 237-247. https://doi.org/10.1016/j.spl.2004.10.037