Annals of the Institute of Statistical Mathematics

, Volume 49, Issue 3, pp 411-434

First online:

Bootstrapping Log Likelihood and EIC, an Extension of AIC

  • Makio IshiguroAffiliated withThe Institute of Statistical Mathematics
  • , Yosiyuki SakamotoAffiliated withThe Institute of Statistical Mathematics
  • , Genshiro KitagawaAffiliated withThe Institute of Statistical Mathematics

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

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