Abstract
The problem of the optimal linear estimation of functionals that depend on the unknown values of the stochastic stationary sequence of observations of a sequence with missing values is considered. Formulas for calculating the root-mean-square error and the spectral characteristic of the optimal linear estimate of the functionals are derived under the spectral determinacy, where the spectral density of the sequence is known exactly. The minimax (robust) method of estimation is applied in the case where the spectral density of the sequence is not known exactly while some classes of feasible spectral densities are given. Formulas that determine the least favourable spectral densities and minimax spectral characteristics are derived for optimal linear estimation of functionals for some special classes of spectral densities.
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Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2022, pp. 128–142.
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Masyutka, O.Y., Moklyachuk, M.P. On Minimax Interpolation of Stationary Sequences. Cybern Syst Anal 58, 268–279 (2022). https://doi.org/10.1007/s10559-022-00459-w
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DOI: https://doi.org/10.1007/s10559-022-00459-w