Asymptotic theory for information criteria in model selection––functional approach

Most of the previously developed information criteria are based on the asymptotic bias correction of the log-likelihood and have common weakness in accuracy and reliability for relatively small sample sizes. We develop a general theory for bias reduction technique in the context of smooth functional statistics and propose an information-theoretic criterion in model evaluation and selection problems. The method can be applied to a wide variety of statistical models obtained by various estimation procedures. The efficiency of the proposed criterion is investigated through a Monte Carlo simulation.