In this paper, the problem of computing the exact value of the asymptotic efficiency of maximum likelihood estimators of 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.
@article{1176324618,
author = {Rubin, Herman and Song, Kai-Sheng},
title = {Exact Computation of the Asymptotic Efficiency of Maximum Likelihood Estimators of a Discontinuous Signal in a Gaussian White Noise},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 732-739},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324618}
}
Rubin, Herman; Song, Kai-Sheng. Exact Computation of the Asymptotic Efficiency of Maximum Likelihood Estimators of a Discontinuous Signal in a Gaussian White Noise. Ann. Statist., Tome 23 (1995) no. 6, pp. 732-739. http://gdmltest.u-ga.fr/item/1176324618/