Abstract
We will consider the problem of determining a linear, mean-square optimal estimate of the transformation\(A\xi = \sum\limits_{j = 0}^\infty {\alpha (j)\xi ( - j)} \) of a stationary random sequence ξ(k) with density f(λ) from observations of the sequence ξ(k) + n(k) withk⩽0, where η(k) is a stationary sequence not correlated with ξ(k) with density g(λ). The least favorable spectral densities
and minimax (robust) spectral characteristics of an optimal estimate Aξ for different classes of densities
are found.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 92–99, January, 1991.
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Moklyachuk, M.P. Minimax filtration of linear transformations of stationary sequences. Ukr Math J 43, 75–81 (1991). https://doi.org/10.1007/BF01066907
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DOI: https://doi.org/10.1007/BF01066907