Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 247-274 |
| Number of pages | 28 |
| Journal | Annals of the Institute of Statistical Mathematics |
| Volume | 71 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Apr 1 2019 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Statistics and Probability
Cite this
AIC for the non-concave penalized likelihood method. / Umezu, Yuta; Shimizu, Yusuke; Masuda, Hiroki; Ninomiya, Yoshiyuki.
In: Annals of the Institute of Statistical Mathematics, Vol. 71, No. 2, 01.04.2019, p. 247-274.Research output: Contribution to journal › Article
}
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
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 -