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Avtomatika i Telemekhanika, 2007, Issue 3, Pages 66–82
(Mi at953)
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This article is cited in 11 scientific papers (total in 11 papers)
Stochastic Systems
Minimax estimation by probabilistic criterion
A. R. Pankov, K. V. Semenikhin Moscow Aviation Institute (State University of Aerospace Technologies)
Abstract:
A minimax estimation problem in multidimensional linear regression model containing uncertain parameters and random quantities is considered. Simultaneous distribution of random quantities that are a part of the observation model is not prescribed exactly; however, it has a fixed mean and a covariance matrix from the given set. For estimation algorithm optimization, we applied a minimax approach with the risk measure in the form of the exceedance probability of the estimate of a prescribed level by an error. It was shown that a linear estimation problem is equivalent to the minimax problem with the mean-square criterion. In addition, the corresponding linear estimate will be the best (in the minimax sense) by the probabilistic criterion at the class of all unbiased estimates. The least favorable distribution of random model parameters is also constructed. Several partial cases and a numerical example are considered.
Citation:
A. R. Pankov, K. V. Semenikhin, “Minimax estimation by probabilistic criterion”, Avtomat. i Telemekh., 2007, no. 3, 66–82; Autom. Remote Control, 68:3 (2007), 430–445
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https://www.mathnet.ru/eng/at953 https://www.mathnet.ru/eng/at/y2007/i3/p66
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Abstract page: | 297 | Full-text PDF : | 115 | References: | 46 | First page: | 1 |
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