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Efficient parametric estimation for a signal-plus-noise Gaussian model from discrete time observations

Author

Listed:
  • Dominique Dehay

    (Univ Rennes)

  • Khalil El Waled

    (University of Nouakchott Al Aasriya
    Qassim University)

  • Vincent Monsan

    (Université Félix Houphouët-Boigny)

Abstract

This paper deals with the parametric inference for integrated continuous time signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional and compounded of a signal-of-interest parameter and a variance parameter of the noise. We state the consistency and the minimax efficiency of the maximum likelihood estimator and of the Bayesian estimator when the time of observation tends to infinity and the delays between two consecutive observations tend to 0 or are only bounded. The class of signals in consideration contains among others, almost periodic signals and also non-continuous periodic signals. However the problem of frequency estimation is not considered here. Furthermore, in this paper the signal-plus-noise discretely observed in time model is considered as a particular case of a more general model of independent Gaussian observations forming a triangular array.

Suggested Citation

  • Dominique Dehay & Khalil El Waled & Vincent Monsan, 2021. "Efficient parametric estimation for a signal-plus-noise Gaussian model from discrete time observations," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 17-33, April.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:1:d:10.1007_s11203-020-09225-1
    DOI: 10.1007/s11203-020-09225-1
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    References listed on IDEAS

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    1. Mishra M.N. & Prakasa Rao B.L.S., 2001. "Asymptotic Minimax Estimation In Nonlinear Stochastic Differential Equations From Discrete Observations," Statistics & Risk Modeling, De Gruyter, vol. 19(2), pages 121-136, February.
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