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[6] [7] 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 .
Equivalently, the estimator achieves equality in the Cramér–Rao inequality for all θ. The Cramér–Rao lower bound is a lower bound of the variance of an unbiased estimator, representing the "best" an unbiased estimator can be. An efficient estimator is also the minimum variance unbiased estimator (MVUE). This is because an efficient ...
For the Cramér–Rao inequality and the Rao–Blackwell theorem see the relevant entries on Earliest Known Uses of Some of the Words of Mathematics; For Rao contribution to information geometry Cramer-Rao Lower Bound and Information Geometry; Photograph of Rao with Harald Cramér in 1978 C. R. Rao from the PORTRAITS OF STATISTICIANS
The quantum Cramér–Rao bound is the quantum analogue of the classical Cramér–Rao bound. It bounds the achievable precision in parameter estimation with a quantum system: It bounds the achievable precision in parameter estimation with a quantum system:
Information inequality may mean in statistics, the Cramér–Rao bound, an inequality for the variance of an estimator based on the information in a sample; in information theory, inequalities in information theory describes various inequalities specific to that context. in sociology, Information Inequality and Social Barriers
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A Rao–Blackwell estimator δ 1 (X) of an unobservable quantity θ is the conditional expected value E(δ(X) | T(X)) of some estimator δ(X) given a sufficient statistic T(X). Call δ( X ) the "original estimator" and δ 1 ( X ) the "improved estimator" .
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