Rao–Blackwell theorem
In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result that characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. The Rao–Blackwell theorem states that if δ ( X ) {\displaystyle \delta (X)} is any kind of estimator of a parameter θ {\displaystyle \theta } , then the conditional expectation of δ ( X ) {\displaystyle \delta (X)} given T ( X ) {\displaystyle T(X)} , where T {\displaystyle T} is a sufficient statistic, is typically a better estimator of θ {\displaystyle \theta } , and is never worse.