ROBUST AND EFFICIENT ALGORITHMS FOR ESTIMATING SIGNALS OF UNKNOWN SHAPE AGAINST THE BACKGROUND OF STATIONARY AND PULSE RANDOM DISTORTIONS
An approach for selecting a model for an adaptive, robust and efficient non-parametric estimation of a signal of unknown shape observed against the background of white noise and pulse interference described by the general non-Gaussian Levy process is presented. Based on that, the structure and characteristics of signal recovery procedures are introduced for the cases of non-asymptotic and asymptotic estimates. First, exact non-asymptotic oracle inequalities for quadratic and robust risks are established, proving that the synthesized estimation procedures are optimal. It is then demonstrated that the application of the obtained oracle inequalities makes it possible to also provide an asymptotic (arising with an unlimited increase in the signal-to-noise ratio) quality to the efficiency of the synthesized estimation algorithms when represented in an adaptive form. The efficiency of the developed procedures as the tools for selecting the model for determining the number of signals in the realization of the observed data is finally illustrated.