Cramer-rao inequality

From HandWiki


This inequality sets a lower limit (the minimum variance bound ) on the uncertainty which can be achieved in the estimation of a parameter . This bound is given by:

File:Hepa img219.gif

where V is the variance (square of the standard deviation), File:Hepa img220.gif bias of the estimator, and Ix is the information about contained in the data X, which can be written:

File:Hepa img221.gif

where L is the likelihood function, and the integral is taken over all the space of the observables X ( Eadie71).