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 . This bound is given by:

where V is the variance (square of the standard deviation), bias of the estimator, and I_x is the information about 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 ( [Eadie71]).