TY - JOUR
T1 - AIC for the non-concave penalized likelihood method
AU - Umezu, Yuta
AU - Shimizu, Yusuke
AU - Masuda, Hiroki
AU - Ninomiya, Yoshiyuki
N1 - Funding Information:
The work of Y. Ninomiya (corresponding author) was partially supported by a Grant-in-Aid for Scientific Research (16K00050) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The works of H. Masuda and Y. Shimizu were partially supported by JST CREST Grant Number JPMJCR14D7, Japan.
Publisher Copyright:
© 2018, The Institute of Statistical Mathematics, Tokyo.
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.
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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 -