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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.