Lehmann–Scheffé theorem

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In statistics, the Lehmann–Scheffé theorem states that any estimator based only on a complete, sufficient statistic is the unique best unbiased estimator of its expected value. The Lehmann–Scheffé theorem is a prominent theory in mathematical statistics, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation.

Formally, if T is a complete sufficient statistic for θ and E(g(T)) = τ(θ) then g(T) is the minimum-variance unbiased estimator (MVUE) for τ(θ))