Asymptotic properties of Hammerstein model estimates

Considers the estimation of Hammerstein models. The main result of the paper lies in a specification of a set of sufficient conditions on the input sequence, the noise (and the true system) in order to ensure that a non-linear least-squares approach enjoys properties of consistency and asymptotic normality and furthermore, that an estimate of the parameter covariance matrix is also consistent. The set of assumptions is specified using the concept of near epoch dependence, which has been developed in the econometrics literature. Indeed, one purpose of the paper is to highlight the usefulness of this concept in the context of analysing estimation procedures for nonlinear dynamical systems. This setup is utilized in an example, where the static nonlinearity is due to input saturation.