Cramér–Rao bound

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In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter. The result is named in honor of Harald Cramér and Calyampudi Radhakrishna Rao, but has also been derived independently by Maurice Fréchet, Georges Darmois, and by Alexander Aitken and Harold Silverstone. It is also known as Fréchet–Cramér–Rao or Fréchet–Darmois–Cramér–Rao lower bound. It states that the precision of any unbiased estimator is at most the Fisher information; or (equivalently) the reciprocal of the Fisher information is a lower bound on its variance. An unbiased estimator that achieves this bound is said to be (fully) efficient. Such a solution achieves the lowest possible mean squared error among all unbiased methods, and is, therefore, the minimum variance unbiased (MVU) estimator. However, in some cases, no unbiased technique exists which achieves the bound. This may occur either if for any unbiased estimator, there exists another...

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