Автор(ы): Добровидов А. В. (ИПУ РАН, Лаборатория 38)Автор(ов): 1 Параметры публикацииТип публикации: Глава в книгеНазвание: Stable Nonparametric Signal Filtration in Nonlinear ModelsISBN/ISSN: ISBN 978-1-4939-0568-3Наименование источника: Topics in Nonparametric StatisticsГород: New YorkИздательство: SpringerГод издания: 2014Страницы: 61-74 АннотацияA stationary two-component markovian process (Xn; Sn)n>1 is considered with the first component observable and the second one non-observable. The problem of filtering a stochastic signal (Sn)n>1 from the mixture with a noise by observations Xn 1 = X1; ¢ ¢ ¢ ;Xn is solved in non-parametric uncertainty regarding the distribution of the desired signal. This means that the probabilistic parametric model of the useful signal (Sn) is assumed to be completely unknown. Under these assumptions, in general, it is impossible to build an optimal Bayesian estimator. However, for a more restricted class of observation models, in which the conditional density f(xnjsn; xn¡1 1 ) belongs to conditionally- exponential family of distribution densities, the Bayesian estimator is a solution of some nonrecurrent equation which depends only on probabilistic characteristics of the observable process (Xn). These unknown characteristics can be restored from observations Xn 1 by using stable non-parametric estimation procedures adapted to dependent data. In detail the nonlinear multiplicative observation model with non-Gaussian noise is considered, and the non-parametric estimator of an unknown gain coefficient is constructed. The results of the model experiment show that the quality of the non-parametric estimator, built for nonlinear observation model, is slightly worse than the quality of the Bayesian estimator (which is naturall), but better than the quality of optimal linear estimator. When building a stable nonparametric procedures the choice of smoothing and regularization parameters plays the crucial role. We propose the optimal choice of these parameters, which leads to an automatic algorithm of non-parametric filtering. Библиографическая ссылка: Добровидов А.В. Stable Nonparametric Signal Filtration in Nonlinear Models / Topics in Nonparametric Statistics. New York: Springer, 2014. С. 61-74.