Abstract
Let ( X1, Y1), ( X2, Y2),…,( X n, Y n) be a random sample of size n from a bivariate normal population with a common mean μ variances [Formula: see text] and [Formula: see text] and correlation coefficient ρ The estimation of the common mean μ has been considered when it is known a priori that the variances are ordered, that is, [Formula: see text] A new estimator has been proposed which dominates the maximum likelihood estimator (without restrictions) stochastically and also in terms of Pitman measure of closeness. Further an inadmissibility condition has been obtained for affine equivariant estimators when the variances are ordered. A numerical comparison of various estimators has been carried out.
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