Sufficient statistic

Summary

A statistic is sufficient for a parameter when it keeps all the information that the sample contains about that parameter. Once its value is known, the rest of the data has a distribution free of the parameter, so it says nothing more about it. Sufficiency allows data reduction without loss, and it underlies the Rao–Blackwell theorem and the theory of optimal estimators. The Fisher–Neyman factorization theorem gives a practical test for it.