Exact Computation of the Asymptotic Efficiency of Maximum Likelihood Estimators of a Discontinuous Signal in a Gaussian White Noise
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.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176324618
Digital Object Identifier: doi:10.1214/aos/1176324618
Mathematical Reviews number (MathSciNet): MR1345196
Zentralblatt MATH identifier: 0838.62020