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

International audience; This paper deals with the parametric inference for integrated continuous time signals embeddedin an additive Gaussian noise and observed at deterministic discrete instants which arenot necessarily equidistant. The unknown parameter ismultidimensional and compounded ofa signal-of-interest parameter and a variance parameter of the noise.We state the consistencyand the minimax efficiency of the maximum likelihood estimator and of the Bayesian estimatorwhen the time of observation tends to infinity and the delays between two consecutiveobservations tend to 0 or are only bounded. The class of signals in consideration containsamong others, almost periodic signals and also non-continuous periodic signals. Howeverthe problem of frequency estimation is not considered here. Furthermore, in this paper thesignal-plus-noise discretely observed in time model is considered as a particular case of amore general model of independent Gaussian observations forming a triangular array.