The Cramér-Rao bound, also called the Cramér-Rao inequality, is a lower bound on the variance of an unbiased
estimator. For an unbiased estimator 
of a scalar parameter 
, the bound is
 |
where 
is the Fisher information in the observations.
More generally, if 
is an unbiased estimator of a differentiable function 
, then
 |
The inequalities require regularity conditions that justify differentiating expectations with respect to 
. They show that greater Fisher
information permits a smaller variance, but they do not guarantee that an estimator
attaining the bound exists.
