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Avtomatika i Telemekhanika, 2017, Issue 10, Pages 90–108
(Mi at14904)
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This article is cited in 2 scientific papers (total in 2 papers)
Stochastic Systems
On sequential confidence estimation of parameters of stochastic dynamical systems with conditionally Gaussian noises
S. E. Vorobeichikov, V. V. Konev Tomsk State University, Tomsk, Russia
Abstract:
We consider the problem of non-asymptotical confidence estimation of linear parameters in multidimensional dynamical systems defined by general regression models with discrete time and conditionally Gaussian noises under the assumption that the number of unknown parameters does not exceed the dimension of the observed process. We develop a non-asymptotical sequential procedure for constructing a confidence region for the vector of unknown parameters with a given diameter and given confidence coefficient that uses a special rule for stopping the observations. A key role in the procedure is played by a novel property established for sequential least squares point estimates earlier proposed by the authors. With a numerical modeling example of a two-dimensional first order autoregression process with random parameters, we illustrate the possibilities for applying confidence estimates to construct adaptive predictions.
Keywords:
confidence estimation, sequential methods for dependent observations, conditionally Gaussian noises, multidimensional dynamical systems, nonlinear time series.
Citation:
S. E. Vorobeichikov, V. V. Konev, “On sequential confidence estimation of parameters of stochastic dynamical systems with conditionally Gaussian noises”, Avtomat. i Telemekh., 2017, no. 10, 90–108; Autom. Remote Control, 78:10 (2017), 1803–1818
Linking options:
https://www.mathnet.ru/eng/at14904 https://www.mathnet.ru/eng/at/y2017/i10/p90
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Abstract page: | 213 | Full-text PDF : | 64 | References: | 32 | First page: | 23 |
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