Data-Based Nonparametric Signal Filtration

Abstract

The problem of stochastic signal filtration under nonparametric uncertainties is considered. A probabilistic description of the signal process is assumed to be completely unknown. The Bayes estimator can not be constructed in this case. However if the conditional density of the observation process given signal process belongs to conditionally exponential family, the optimal Bayes estimator is a solution to some non-recurrent equation which is explicitly independent upon the signal process distribution. In this case, the Bayes estimator is expressed in terms of conditional distribution of the observation process, which can be approximated by using of the stable nonparametric procedures, adapted to dependent samples. These stable approximations provide the mean square convergence to Bayes estimator. In the stable kernel nonparametric procedures, a crucial step is to select a proper smoothing parameter (bandwidth) and a regularized parameter, which have a considerable influence on the quality of signal filtration. The optimal procedures for selecting of these parameters are proposed. These procedures allow to construct the automatic (data-based) signal filtration algorithm.