Bootstrapping Likelihood for Model Selection with Small Samples

Akaike s Information Criterion AIC derived from asymptotics of the maximum like lihood estimator is widely used in model selection However it has a nite sample bias which produces over tting in linear regression To deal with this problem Ishiguro et al proposed a bootstrap based extension to AIC which they call EIC In this report we compare model selection performance of AIC EIC a bootstrap smoothed likelihood cross validation BCV and its modi cation CV in small sample linear regression logistic regression and Cox regression Simulation results show that EIC largely overcomes AIC s over tting problem and that BCV may be better than EIC Hence the three methods based on bootstrapping the likelihood establish themselves as important alternatives to AIC in model selection with small samples