## Annals of Statistics

### Exact Computation of the Asymptotic Efficiency of Maximum Likelihood Estimators of a Discontinuous Signal in a Gaussian White Noise

#### Abstract

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 information

Source
Ann. Statist., Volume 23, Number 3 (1995), 732-739.

Dates
First available in Project Euclid: 11 April 2007

https://projecteuclid.org/euclid.aos/1176324618

Digital Object Identifier
doi:10.1214/aos/1176324618

Mathematical Reviews number (MathSciNet)
MR1345196

Zentralblatt MATH identifier
0838.62020

JSTOR