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AN EFFICIENT ESTIMATOR FOR THE EXPECTATION

OF A BOUNDED FUNCTION UNDER THE RESIDUAL

DISTRIBUTION OF AN AUTOREGRESSIVE PROCESS

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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.

**Source**
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