EXACT COMPUTATION OF THE ASYMPTOTIC EFFICIENCY OF MAXIMUM LIKELIHOOD ESTIMATORS OF A DISCONTINUOUS SIGNAL IN A GAUSSIAN WHITE NOISE

摘要

In this paper, the problem of computing the exact value of the asymptotic efficiency of maximum likelihood estimators ol a discontinuous signal in a Gaussian white noise is considered. A method based on constructing difference equations for the appropriate moments is presented and used to show that the exact variance of the Pitman estimator is 16 zeta(3), where zeta is the Riemann zeta function. [References: 5]