Asymptotic Properties of a Class of Criteria for Best Model Selection

摘要

The paper investigates the asymptotic convergence of some typical criteria for model selection from a given data sample. A range of known criteria are generalized into a special class joining two different groups based on both explicit and implicit implementing the trade-off between model accuracy and complexity. Criteria of the first group contain various explicit penalty terms for the model complexity whereas those from the second group are based on the sample division into two parts which is typical for the GMDH criteria. Definitions of asymptotic characteristics of the criteria are given and analyzed as well as the fact of consistency of such generalized class of criteria under some sufficient conditions regarding input vectors is proved.