Annals of Statistics

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

Herman Rubin and Kai-Sheng Song

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 60J65: Brownian motion [See also 58J65]

Keywords
Brownian motion change-point efficiency Pitman estimator

Citation

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. 23 (1995), no. 3, 732--739. doi:10.1214/aos/1176324618. https://projecteuclid.org/euclid.aos/1176324618


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