Estimation non paramétrique dans un modèle autorégressif fonctionnel non directement observé

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In this Note, we are interested in the nonparametric estimation of the regression function of a functional autoregressive model of order 1, the state of which is not directly observed. We prove that the associated kernel estimator is biased and converges almost surely to a function, which depends on the unknown autoregressive function and on the observation noise distribution. If the observation noise variance tends to 0, we prove the consistency of the kernel estimator.