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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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