Cramer-Rao Bound

In estimation theory and statistics, the Cramer-Rao bound relates to the estimation of a fixed but unknown parameter, and it states that the precision of any unbiased estimator is at most the Fisher information, or equivalently that the reciprocal of the Fisher information is a lower bound on the estimator's variance. The result is named for Harald Cramer and Calyampudi Radhakrishna Rao, though Maurice Frechet, Georges Darmois, Alexander Aitken and Harold Silverstone each derived it independently, and an estimator that achieves the bound is called fully efficient because it attains the lowest possible mean squared error among unbiased methods.