### Abstract

Change-point problems have been studied for a long time not only because they are needed in various fields but also because change-point models contain an irregularity that requires an alternative to conventional asymptotic theory. The purpose of this study is to derive the AIC for such change-point models. The penalty term of the AIC is twice the asymptotic bias of the maximum log-likelihood, whereas it is twice the number of parameters, $$2p_0$$2p0, in regular models. In change-point models, it is not twice the number of parameters, $$2m+2p_m$$2m+2pm, because of their irregularity, where $$m$$m and $$p_m$$pm are the numbers of the change-points and the other parameters, respectively. In this study, the asymptotic bias is shown to become $$6m+2p_m$$6m+2pm, which is simple enough to conduct an easy change-point model selection. Moreover, the validity of the AIC is demonstrated using simulation studies.

Original language | English |
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Pages (from-to) | 943-961 |

Number of pages | 19 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 67 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 26 2015 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability

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## Cite this

*Annals of the Institute of Statistical Mathematics*,

*67*(5), 943-961. https://doi.org/10.1007/s10463-014-0481-x