Generalised information criteria in model selection

The problem of evaluating the goodness of statistical models is investigated from an information-theoretic point of view. Information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data. The proposed criteria are applied to the evaluation of models estimated by maximum likelihood, robust, penahsed likelihood, Bayes procedures, etc. We also discuss the use of the bootstrap in model evaluation problems and present a variance reduction technique in the bootstrap simulation.