Parametric and nonparametric curve fitting

We are concerned with convergence issues in the identification of a static nonlinear function. Our investigation focuses on properties of the input signal that ensure convergence of the estimate. Both parametric and nonparametric approaches are considered. In the parametric case, we offer sufficient conditions under which the estimated parameters converge to their true values almost surely. For the nonparametric case, we offer necessary and sufficient conditions under which the estimated function converges almost surely to the true nonlinearity.