##  [Cramér–Rao Lower Bound](/index.php/cramer-rao-lower-bound) 

  ##  [Cramér–Rao Lower Bound](https://mathlogic.quantumdictionary.io/cramer-rao-lower-bound-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A lower bound on the variance (or covariance matrix) of any unbiased estimator of a parameter, expressed in terms of the Fisher information: for a scalar parameter, Var(theta_hat) >= 1 / I(theta); in multivariate form the covariance matrix is bounded below by the inverse Fisher information matrix under regularity conditions.