Automatic methods of useful signals extraction from noise background under conditions of nonparametric uncertainty

Three basic techniques for random signals processing are under study: the problems of filtration, interpolation, and prediction. The last advances (including those of the author) in finding smoothing parameter (bandwidth) in the problems of nonparametric kernel estimation of unknown probability densities and their derivatives made it possible to advance further in the theory of the nonparametric estimation of signals with unknown distribution. This progress gave rise to the evolution of automatic methods for signals extraction from noise under the conditions of nonparametric uncertainty. The word “automatic” is understood in the sense that the suggested methods for processing signals depend only on the observable sample. In the article, by the simple example of the additive model, the comparison is made of the nonparametric procedures for the signals processing with the known optimal processing procedures obtained at the complete statistical information about the signals and noise distributions. The results of computer modeling show that the accuracy of nonparametric signals estimates insignificantly gives up to the accuracy of optimal estimates.