Lehmann–Scheffé theorem

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In statistics, the Lehmann–Scheffé theorem states the any estimator that is complete, sufficient, and unbiased is the unique best unbiased estimator of its expectation. The Lehmann-Scheffé Theorem states that if a complete and sufficient statistic T exists, then the UMVU estimator of g(θ) (if it exists) must be a function of T. The Lehmann-Scheffe Theorem also simplifies the search for unbiased estimators considerably: if a complete and sufficient statistic T exists and there exists no function h such that E_θ[h(T)] = g(θ) then no unbiased estimator of g(θ) exists.

The usual way to find such an estimator is application of the Rao–Blackwell theorem.