The Cramer-Rao Inequality gives a lower bound on the variance of any unbiased estimator of a parameter, stating that the variance can never be smaller than the reciprocal of the Fisher information for that parameter. Named for Harald Cramer and Calyampudi Radhakrishna Rao, it is a foundational result of statistical estimation theory used to judge how efficient an estimator can possibly be.
Facts
StatementThe precision of any unbiased estimator is at most the Fisher information; equivalently, the reciprocal of the Fisher information is a lower bound on its variance. 1 Classification
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Source Cramer-Rao inequality (bound), Wikipedia
Source Cramer-Rao inequality (bound), Wikipedia
Sources
1. Cramer-Rao inequality (bound), Wikipedia
Lead paragraph
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.
In Group: Mathematical Statistics and Estimation, Lead
In estimation theory and statistics, the Cramér-Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter.
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