Adaptive estimation in a random coefficient autoregressive model

This paper proves the local asymptotic normality of a stationary and ergodic first order random coefficient autoregressive model in a semiparametric setting. This result is used to show that Stein's necessary condition for adaptive estimation of the mean of the random coefficient is satisfied if the distributions of the innovations and the errors in the random coefficients are symmetric around zero. Under these symmetry assumptions, a locally asymptotically minimax adaptive estimator of the mean of the random coefficient is constructed. The paper also proves the asymptotic normality of generalized M-estimators of the parameter of interest. These estimators are used as preliminary estimators in the above construction.