High Quality Content by WIKIPEDIA articles! In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result which 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 g(X) is any kind of estimator of a parameter ?, then the conditional expectation of g(X) given T(X), where T is a sufficient statistic, is typically a better estimator of ?, and is never worse. Sometimes one can very easily construct a very crude estimator g(X), and then evaluate that conditional expected value to get an estimator that is in various senses optimal.

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