Adaptive R-Estimation in Autoregressions

Abstract

In this paper we explore the local asymptotic normality property with a ranked residual central sequence in autoregression to give locally asymptotically minimax estimators of the autoregressive parameter. Then, we use the kernel estimator method described by Koul and Schick [Koul, H. L., Schick, A. (1997). Efficient estimation in nonlinear autoregressive time series models. Bernoulli 3:247–277] to construct adaptive estimators. A simulation experiment is carried out to illustrate the performance of the proposed adaptive estimators.