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

Dominique Dehay (), Khalil El Waled () and Vincent Monsan ()
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Dominique Dehay: Univ Rennes
Khalil El Waled: University of Nouakchott Al Aasriya
Vincent Monsan: Université Félix Houphouët-Boigny

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 1, No 2, 17-33

Abstract: 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.

Keywords: Maximum likelihood estimation; Bayesian estimation; High frequency sampling; Low frequency sampling; Minimax efficiency; Asymptotic properties of estimators; Triangular Gaussian array; Hellinger distance (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11203-020-09225-1

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