A Structural Analysis of Criteria for Selecting Model Variables

A means of analyzing the structure of criteria for selecting model variables (selection criteria) which are expressed by scalar products of differences among the sample vector of the object to be modeled and the output vectors of its models is shown. The relations between the above scalar products and the known selection criteria are given and new quantities to be used as selection criteria are found. Two different view-points on the fitness of a model are presented. On the basis of the viewpoints, the asymmetric fitting characteristic vector (AFCV) and the symmetric fitting characteristic vector (SFCV) are developed as tools for analyzing the structure of the selection criteria. The relations between the AFCV and the coefficients of a model are presented. Based on the relations, a new method of applying the least squares method to a model without a constant term is proposed. New selection criteria are proposed on the basis of the structural analysis. The basic relation between the regularity criterion and the absence-of-bias criterion which are used in the group method of data handling (GMDH) is clarified with the structural analysis.