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