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Exact computation of the asymptotic efficiency of maximum likelihood estimators of a discontinuous signal in a Gaussian white noise. (English) Zbl 0838.62020
Summary: 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.

##### MSC:
 62F12 Asymptotic properties of parametric estimators 62M05 Markov processes: estimation; hidden Markov models
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