Estimation in autoregressive model with measurement error

Consider an autoregressive model with measurement error: we observe Zi = Xi + εi, where Xi is a stationary solution of the autoregressive equation Xi = fθ0(Xi−1) + ξi. The regression function fθ0 is known up to a finite dimensional parameter θ. The distributions of X0 and ξ1 are unknown whereas the distribution of ε0 is completely known. We want to estimate the parameter θ by using the observations Z0, . . . , Zn. We propose an estimation procedure based on a modified least square criterion. This procedure provides an asymptotically normal estimator θ̂ of θ, for a large class of regression functions and various noise distributions.