### 抄録

Non-concave penalized maximum likelihood methods are widely used because they are more efficient than the Lasso. They include a tuning parameter which controls a penalty level, and several information criteria have been developed for selecting it. While these criteria assure the model selection consistency, they have a problem in that there are no appropriate rules for choosing one from the class of information criteria satisfying such a preferred asymptotic property. In this paper, we derive an information criterion based on the original definition of the AIC by considering minimization of the prediction error rather than model selection consistency. Concretely speaking, we derive a function of the score statistic that is asymptotically equivalent to the non-concave penalized maximum likelihood estimator and then provide an estimator of the Kullback–Leibler divergence between the true distribution and the estimated distribution based on the function, whose bias converges in mean to zero.

元の言語 | 英語 |
---|---|

ページ（範囲） | 247-274 |

ページ数 | 28 |

ジャーナル | Annals of the Institute of Statistical Mathematics |

巻 | 71 |

発行部数 | 2 |

DOI | |

出版物ステータス | 出版済み - 4 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### これを引用

*Annals of the Institute of Statistical Mathematics*,

*71*(2), 247-274. https://doi.org/10.1007/s10463-018-0649-x

**AIC for the non-concave penalized likelihood method.** / Umezu, Yuta; Shimizu, Yusuke; Masuda, Hiroki; Ninomiya, Yoshiyuki.

研究成果: ジャーナルへの寄稿 › 記事

*Annals of the Institute of Statistical Mathematics*, 巻. 71, 番号 2, pp. 247-274. https://doi.org/10.1007/s10463-018-0649-x

}

TY - JOUR

T1 - AIC for the non-concave penalized likelihood method

AU - Umezu, Yuta

AU - Shimizu, Yusuke

AU - Masuda, Hiroki

AU - Ninomiya, Yoshiyuki

PY - 2019/4/1

Y1 - 2019/4/1

N2 - Non-concave penalized maximum likelihood methods are widely used because they are more efficient than the Lasso. They include a tuning parameter which controls a penalty level, and several information criteria have been developed for selecting it. While these criteria assure the model selection consistency, they have a problem in that there are no appropriate rules for choosing one from the class of information criteria satisfying such a preferred asymptotic property. In this paper, we derive an information criterion based on the original definition of the AIC by considering minimization of the prediction error rather than model selection consistency. Concretely speaking, we derive a function of the score statistic that is asymptotically equivalent to the non-concave penalized maximum likelihood estimator and then provide an estimator of the Kullback–Leibler divergence between the true distribution and the estimated distribution based on the function, whose bias converges in mean to zero.

AB - Non-concave penalized maximum likelihood methods are widely used because they are more efficient than the Lasso. They include a tuning parameter which controls a penalty level, and several information criteria have been developed for selecting it. While these criteria assure the model selection consistency, they have a problem in that there are no appropriate rules for choosing one from the class of information criteria satisfying such a preferred asymptotic property. In this paper, we derive an information criterion based on the original definition of the AIC by considering minimization of the prediction error rather than model selection consistency. Concretely speaking, we derive a function of the score statistic that is asymptotically equivalent to the non-concave penalized maximum likelihood estimator and then provide an estimator of the Kullback–Leibler divergence between the true distribution and the estimated distribution based on the function, whose bias converges in mean to zero.

UR - http://www.scopus.com/inward/record.url?scp=85042626489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042626489&partnerID=8YFLogxK

U2 - 10.1007/s10463-018-0649-x

DO - 10.1007/s10463-018-0649-x

M3 - Article

AN - SCOPUS:85042626489

VL - 71

SP - 247

EP - 274

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 2

ER -