Abstract
Abstract Determining the minimum variance of an unbiased estimator constitutes a fundamental topic in mathematical statistics. Two primary results are the Cramér–Rao inequality, which gives a lower bound on the variance of an unbiased estimator, and the Rao–Blackwell theorem, which supplies a method for improving the variance of unbiased estimators that are not functions of sufficient statistics. The strongest results are available for sufficient statistics from complete exponential families. However, any functions of sufficient statistics will attain the Cramér–Rao lower bound for sufficiently large sample sizes.
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