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(ii) Suppose that T = h(T˜), where T˜ is a sufficient statistic for P ∈ P and h is a Borel function Let UT˜ be the subset of U consisting of Borel functions of T˜ Then a necessary and sufficient condition for T to be a UMVUE of ϑ is that ET(X)U(X) = 0 for any U ∈ UT˜ and any P ∈ P Proof (i) Suppose that T is a UMVUE of ϑ.
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