A Note on Minimum Variance Unbiased Estimation

The process of Rao–Blackwellization involves specification of a naïve unbiased estimator of τ(θ) and then determination of its conditional expectation given a complete and sufficient statistic T for θ. This leads to the minimum variance unbiased estimator (MVUE) U ≡ U(T) for τ(θ). In some situations, however, a naïve unbiased estimator of τ(θ) may not be an easy thing to come across. Theorem 2.1 fills an important void by formulating a new approach to find the MVUE for τ(θ) in a number of interesting situations where the customary Rao–Blackwellization technique may not be very simple to implement. The new approach is illustrated with the help of a series of interesting examples. Theorem 2.1 has its own limitation and we have highlighted that with an example.