On estimation of discrete Hammerstein system by nonparametric regression estimate

In this paper we discuss estimation of discrete Hammerstein system with initial conditions. We obtain the auto-correlation function as well as parameters of dynamic linear subsystem by the correlation method. No conditions whatsover are imposed on the transform characteristics of nonlinear, memoryless subsystem with multivariate input and single output. The estimation algorithm is given and its local as well as global distribution- free convergence is shown as the number of measurements tends to infinity. The rates of convergence in both cases are derived under mild conditions on the smoothness of nonlinear system.