Ukrainian Mathematical Journal

, Volume 43, Issue 1, pp 75–81 | Cite as

Minimax filtration of linear transformations of stationary sequences

  • M. P. Moklyachuk
Article

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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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • M. P. Moklyachuk
    • 1
  1. 1.Kiev UniversityUSSR

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