Lehmann–Scheffé theorem
= Lehmann–Scheffé theorem
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An unbiased <estimator> that is a function of a <complete sufficient statistic> is the unique uniformly minimum-<variance> unbiased <estimator>, up to almost sure equality. <Rao-Blackwellization> supplies <variance> reduction, and completeness supplies uniqueness. The theorem applies to a conditional statistical experiment as well, when unbiasedness, sufficiency and completeness are all evaluated under that conditional family.