On parameter estimation for cusp-type signals |
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| Authors: | O. V. Chernoyarov S. Dachian Yu. A. Kutoyants |
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| Affiliation: | 1.Department of Radio Engineering Devices and Antenna Systems,National Research University “MPEI”,Moscow,Russia;2.Laboratoire Paul Painlevé, UMR CNRS 8524, Cité Scientifique,Villeneuve d’Ascq Cedex,France;3.Laboratoire Manceau de Mathématiques,Université du Maine,Le Mans Cedex 9,France |
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| Abstract: | We consider the problem of parameter estimation by continuous time observations of a deterministic signal in white Gaussian noise. It is supposed that the signal has a cusp-type singularity. The properties of the maximum-likelihood and Bayesian estimators are described in the asymptotics of small noise. Special attention is paid to the problem of parameter estimation in the situation of misspecification in regularity, i.e., when the statistician supposes that the observed signal has this singularity, but the real signal is smooth. The rate and the asymptotic distribution of the maximum-likelihood estimator in this situation are described. |
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