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On parameter estimation for cusp-type signals

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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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Acknowledgments

We are grateful to the Referees for their useful comments. This work was done under partial financial support of the Grant of RSF Number 14-49-00079.

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Authors and Affiliations

  1. Department of Radio Engineering Devices and Antenna Systems, National Research University “MPEI”, 14 Krasnokazarmennaya st., 111250, Moscow, Russia

    O. V. Chernoyarov, S. Dachian & Yu. A. Kutoyants

  2. Laboratoire Paul Painlevé, UMR CNRS 8524, Cité Scientifique, Université de Lille 1, 59655, Villeneuve d’Ascq Cedex, France

    S. Dachian

  3. Laboratoire Manceau de Mathématiques, Université du Maine, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France

    Yu. A. Kutoyants

Authors
  1. O. V. Chernoyarov
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  2. S. Dachian
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  3. Yu. A. Kutoyants
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Correspondence to Yu. A. Kutoyants.

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Chernoyarov, O.V., Dachian, S. & Kutoyants, Y.A. On parameter estimation for cusp-type signals. Ann Inst Stat Math 70, 39–62 (2018). https://doi.org/10.1007/s10463-016-0581-x

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  • DOI: https://doi.org/10.1007/s10463-016-0581-x

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