AN EFFICIENT ESTIMATOR FOR THE EXPECTATION OF A BOUNDED FUNCTION UNDER THE RESIDUAL DISTRIBUTION OF AN AUTOREGRESSIVE PROCESS

W. WEFELMEYER

Mathematical Institute, University of Cologne, Weyertal 86, 50931 Cologne, Germany

(Received December 18, 1992; revised August 18, 1993)

Abstract. Consider a stationary first-order autoregressive process, with i.i.d. residuals following an unknown mean zero distribution. The customary estimator for the expectation of a bounded function under the residual distribution is the empirical estimator based on the estimated residuals. We show that this estimator is not efficient, and construct a simple efficient estimator. It is adaptive with respect to the autoregression parameter.

Key words and phrases: Autoregressive model, efficient estimator, empirical estimator, residual distribution.