Bootstrap choice of estimators in parametric and semiparametric families: an extension of EIC

Ishiguro, Sakamoto, and Kitagawa (1997, Annals of the Institute of Statistical Mathematics 49, 411-434) proposed EIC as an extension of Akaike criterion (AIC); the idea leading to EIC is to correct the bias of the log-likelihood, considered as an estimator of the Kullback-Leibler information, using bootstrap. We develop this criterion for its use in multivariate semiparametric situations, and argue that it can be used for choosing among parametric and semiparametric estimators. A simulation study based on aregression model shows that EIC is better than its competitors although likelihood cross-validation performs nearly as well except for small sample size. Its use is illustrated by estimating the mean evolution of viral RNA levels in a group of infants infected by HIV.