Bandwidth Selection for Kernel Generalized Regression Neural Networks in Identification of Hammerstein Systems

Abstract

Abstract This paper addresses the issue of data-driven smoothing parameter (bandwidth) selection in the context of nonparametric system identification of dynamic systems. In particular, we examine the identification problem of the block-oriented Hammerstein cascade system. A class of kernel-type Generalized Regression Neural Networks (GRNN) is employed as the identification algorithm. The statistical accuracy of the kernel GRNN estimate is critically influenced by the choice of the bandwidth. Given the need of data-driven bandwidth specification we propose several automatic selection methods that are compared by means of simulation studies. Our experiments reveal that the method referred to as the partitioned cross-validation algorithm can be recommended as the practical procedure for the bandwidth choice for the kernel GRNN estimate in terms of its statistical accuracy and implementation aspects.