Applicational possibilities of nonparametric estimation

Abstract. Together with the dynamic development of modern computer systems, the possibilities of applying refined methods of nonpara-metric estimation to control engineering tasks have grown just as fast. This broad and complex theme is presented in this paper for the case of estimation of density of a random variable distribution. Nonparametric methods allow here the useful characterization of probability distributions without arbitrary assumptions regarding their membership to a fixed class. Following an illustratory description of the funda-mental procedures used to this end, results will be generalized and synthetically presented of research on the application of kernel estimators, dominant here, in problems of Bayes parameter estimation with asymmetrical polynomial loss function, as well as for fault detection in dynamical systems as objects of automatic control, in the scope of detection, diagnosis and prognosis of malfunctions. To this aim the basics of data analysis and exploration tasks – recognition of outliers, clustering and classification – solved using uniform mathematical apparatus based on the kernel estimators methodology were also investigated. Key words: control engineering, nonparametric estimation, density of probability distribution, kernel estimators, data analysis and explo-ration, Bayes parameter estimation, fault detection, optimal control, robust control. 1