Estimation in autoregressive model with measurement error

Consider an autoregressive model with measurement error: we observe Zi = Xi + εi, where the unobserved Xi is a stationary solution of the autoregressive equation Xi = gθ0(Xi − 1) + ξi. The regression function gθ0 is known up to a finite dimensional parameter θ0 to be estimated. The distributions of ξ1 and X0 are unknown and gθ belongs to a large class of parametric regression functions. The distribution of ε0 is completely known. We propose an estimation procedure with a new criterion computed as the Fourier transform of a weighted least square contrast. This procedure provides an asymptotically normal estimator \hbox{$\hat \theta$} of θ0, for a large class of regression functions and various noise distributions