Abstract
The Rao-Blackwell theorem is one of the most important theorems in mathematical statistics. It asserts that any unbiased estimator is improved w.r.t. variance by an unbiased estimator which is a function of a sufficient statistic. Hence the class of unbiased estimators which are functions of a sufficient statistic constitutes an essentially complete class. However such a ”Rao-Blackwellization” of an unbiased estimator does not necessarily provide a UMVU (uniformly minimum variance unbiased) estimator. Lehmann and Scheffe (1950) showed that if there exists a complete sufficient statistic then the Rao-Blackwellization w.r.t. the statistic produces a UMVU estimator.
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