AIC for the non-concave penalized likelihood method

Yuta Umezu, Yusuke Shimizu, Hiroki Masuda, Yoshiyuki Ninomiya

研究成果: Contribution to journalArticle

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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
71
発行部数2
DOI
出版物ステータス出版済み - 4 1 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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