Estimation of autoregressive coefficient in an ARMA (1,1) model with vague information on the MA component

In this paper we investigate the asymptotic properties of various estimators of
autocorrelation parameter of an ARMA(1,1) model when uncertain non{sample
prior information on the moving average component is available. In particular we
study the preliminary test and the shrinkage estimators of the autocorrelation parameter
and we compare their efficiency with respect to the maximum likelihood
estimator designated as the unrestricted estimator. It is shown that near the prior
information on MA-parameter, both preliminary test and shrinkage estimators
are superior to the MLE while they lose their superiority as the MA-parameter
moves away from the prior information although preliminary test estimator gains
its effciency to some extent but the shrinkage estimator attains its lower bound
of its efficiency.