  Consider an autoregressive model with measurement error: we observe
$Z_i=X_i+\epsilon_i$, where $X_i$ is a stationary solution of the equation
$X_i=f_{\theta^0}(X_{i-1})+\xi_i$. The regression function $f_{\theta^0}$ is
known up to a finite dimensional parameter $\theta^0$. The distributions of
$X_0$ and $\xi_1$ are unknown whereas the distribution of $\epsilon_1$ is
completely known. We want to estimate the parameter $\theta^0$ by using the
observations $Z_0,..,Z_n$. We propose an estimation procedure based on a
modified least square criterion involving a weight function $w$, to be suitably
chosen. We give upper bounds for the risk of the estimator, which depend on the
smoothness of the errors density $f_\epsilon$ and on the smoothness properties
of $w f_\theta$.
