Bootstrapping log likelihood and EIC, an extension of AIC

被引：82

作者：

Ishiguro, M ^{[1
]}

Sakamoto, Y ^{[1
]}

Kitagawa, G ^{[1
]}

机构：

[1] INST STAT MATH,MINATO KU,MINATO KU,TOKYO 106,JAPAN

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 1997年 / 49卷 / 03期

关键词：

log likelihood; AIC; bootstrap; MLE; information criterion; model selection; estimator selection; bias correction; expected log likelihood; penalized log likelihood; predictive distribution;

D O I：

10.1023/A:1003158526504

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Akaike (1973, 2nd International Symposium on Information Theory, 267-281, Akademiai Kiado, Budapest) proposed AIC as an estimate of the expected log likelihood to evaluate the goodness of models fitted to a given set of data. The introduction of AIC has greatly widened the range of application of statistical methods. However, its limit lies in the point that it can be applied only to the cases where the parameter estimation are performed by the maximum likelihood method. The derivation of AIC is based on the assessment of the effect of data fluctuation through the asymptotic normality of MLE. In this paper we propose a new information criterion EIC which is constructed by employing the bootstrap method to simulate the data fluctuation. The new information criterion, EIC, is regarded as an extension of AIC. The performance of EIC is demonstrated by some numerical examples.

引用

页码：411 / 434

页数：24

共 13 条

[1]

Akaike H., 1973, 2 INT S INFORM THEOR, P267, DOI [10.1007/978-1-4612-1694-0_15, DOI 10.1007/978-1-4612-1694-0_15]

[2]

Akaike H., 1980, BAYESIAN STAT, P143, DOI [DOI 10.1007/BF02888350, DOI 10.1007/978-1-4612-1694-0_24]

[3] 1977 RIETZ LECTURE - BOOTSTRAP METHODS - ANOTHER LOOK AT THE JACKKNIFE [J].