Estimation of the common mean of two univariate normal populations

The problem of estimating the common mean μ of two univariate normal populations with unknown and unequal variances is considered from a decision-theoretic point of view. We restrict our attention to an appropriate class C and its three subclasses C0C1C2of un-biased estimates of μ. We consider the usual estimate μ0 of μ which is the weighted linear combination of the sample means with weights as reciprocals of the sample variances. Its admissibility in C0 and extended admissibility in C is proved. Admissible estimates in C1 and C2are also obtained.The loss is always assumed to be squared error. The question of admissibility of μ0 in the class of all estimators is still open.