https://elib.bsu.by:443/handle/123456789/94270 Tue, 21 Apr 2026 07:21:47 GMT 2026-04-21T07:21:47Z https://elib.bsu.by:443/handle/123456789/94349 Заглавие документа: Nonparametric analysis of stochastic systems with nonlinear functional heterogeneity Авторы: Malugin, V. I.; Vasilkov, M. E. Аннотация: The problems of the analysis of stochastic systems described by nonlinear statistical models with heterogeneous functional forms are considered. It is supposed that functional heterogeneity is conditioned by the existing of the different classes of system states. Moreover it being known that every state of a system characterized by un-known nonlinear models, that are different for different classes of states. The methods of estimation and forecasting of the systems states based on multivariate nonparametric density estimate with variable kernel are suggested and examined by means of asymptotic expansions of the conditional risk as well as by statistical modeling experiments. Fri, 01 Jan 2010 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/94349 2010-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/94348 Заглавие документа: Optimal predictions of powers of conditionally heteroskedastic processes Авторы: Francq, C.; Zakoian, J.-M. Аннотация: The standard method for estimating powers of conditionally heteroskedastic processes is a two-step procedure in which the volatility is estimated by ga.us-sian quasi-maximum likelihood (QML) in a first step, and an empirical mean of the rescaled innovations is computed in a second step. This paper proposes an alternative one-step procedure, based on an appropriate non-gaussian QML estimation of the model, and establishes the asymptotic properties of the two ap¬proaches. Their performances are compared for finite-order GARCH models and for the ARCH(oo). For the standard GARCH(p, q) and the Asymmetric Power GARCH(p, g), it is shown that the asymptotic relative efficiency of the estimators only depends on the prediction problem and on some moments of the independent process. An application to indexes of major stock exchanges is proposed. Fri, 01 Jan 2010 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/94348 2010-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/94347 Заглавие документа: Fuzzy Bayesian inference Авторы: Viertl, R. Аннотация: Data are frequently not precise numbers but more or less non-precise, also called fuzzy. Moreover a-priori information in Bayesian inference is usually not available as a precise probability distribution. In case of fuzzy data and fuzzy a-priori information Bayes' theorem has to be generalized. There are different approaches for a generalization of Bayes' theorem but most of them don't keep the sequential updating of standard Bayesian inference. A generalization taking care of this is possible and will be explained in the talk. Also an alternative definition of fuzzy predictive distributions based on the so-called fuzzy probability integral will be given. Fri, 01 Jan 2010 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/94347 2010-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/94346 Заглавие документа: On the joint distribution of precedences and exceedances for the two-sample problem Авторы: Stoimenova E. E.; Balakrishnan, N. Аннотация: This paper concerns the joint behaviour of precedences of one sample with respect to a threshold from the other sample and exceedances of second sample with respect to a threshold from the Їrst sample. Exact distributions under the same distribution of the samples and under stochastically ordered distributions are obtained. Fri, 01 Jan 2010 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/94346 2010-01-01T00:00:00Z