Cramer-rao inequality

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

Error creating thumbnail: Unable to save thumbnail to destination

. This bound is given by:

where V is the variance (square of the standard deviation), File:Hepa img220.gif bias of the estimator, and I_x is the information about

Error creating thumbnail: Unable to save thumbnail to destination

contained in the data X, which can be written:

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

Error creating thumbnail: Unable to save thumbnail to destination

Eadie71).