On Asymptotic Properties of the GMDH Criteria

The paper analyses the problem of the convergence investigation for typical GMDH criteria based on the data sample division into two subsamples. This study is significant for additional justification of applying the GMDH-based inductive modeling in case of large samples. The inductive modeling problem is defined and main external criteria are presented. An approach to the asymptotic investigations is explained based on assumptions of strong regularity of regressors. The study results demonstrate the convergence of any external criterion to some finite values in probability. Moreover, the minimal value of an accuracy criterion at infinity corresponds to the true model. This means that such criteria are consistent.