ABSTRACT
Let a design p be given and consider a p-unbiased estimator t, that is, Bp(t) = Ep(t − Y ) = 0 uniformly in Y . The performance of such an estimator is assessed by V p(t) = Ep(t − Y )2 and we would like to minimize V p(t) uniformly in Y . Assume t∗ is such a uniformly minimum variance (UMV) unbiased estimator (UMVUE), that is, for every unbiased t (other than t∗) one has V p(t∗) ≤ V p(t) for every Y and V p(t∗) < V p(t) at least for one Y .
