Editing Lehmann–Scheffé theorem (section)

{{Short description|Theorem in statistics}}
{{Refimprove|date=April 2011}}
In [[statistics]], the '''Lehmann–Scheffé theorem''' is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation.<ref name=Casella/> The theorem states that any [[estimator]] that is [[unbiased estimator|unbiased]] for a given unknown quantity and that depends on the data only through a [[completeness (statistics)|complete]], [[sufficiency (statistics)|sufficient statistic]] is the unique [[best unbiased estimator]] of that quantity. The Lehmann–Scheffé theorem is named after [[Erich Leo Lehmann]] and [[Henry Scheffé]], given their two early papers.<ref name=LS1/><ref name=LS2/>

If <math> T </math> is a complete sufficient statistic for <math> \theta </math> and <math>\operatorname{E}[g(T)]=\tau(\theta) </math> then <math>g(T)</math> is the [[uniformly minimum-variance unbiased estimator]] (UMVUE) of <math>\tau(\theta)</math>.