(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.
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