The characteristics of a biased estimator applied to the adaptive GMDH

Abstract

In this paper, the characteristics of the ridge biased estimator obtained in the adaptive GMDH (Group Method of Data Handling), which applies the ridge bias parameter to a system identification procedure is discussed. Using the canonical model based on the generalized ridge estimator, the stability and shrinkability of the ridge estimator depends on certain convergence conditions, which are described and examined with the relationships of the iterative procedure for obtaining an optimal estimator. Furthermore, it is shown that a principal component estimator is included in the ridge estimator in the adaptive GMDH.