Filtering Problem for Stationary Sequences with Missing Observations

  • Mikhail Moklyachuk Kyiv National Taras Shevchenko University
  • Maria Sidei Kyiv National Taras Shevchenko University
Keywords: Stationary sequence, mean square error, minimax-robust estimate, least favorable spectral density, minimax spectral characteristic

Abstract

We deal with the problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with a stationary noise sequence. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived under the condition of spectral certainty, where spectral densities of the sequences are exactly known. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities are not known exactly while sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed for some special sets of admissible densities.

Author Biography

Mikhail Moklyachuk, Kyiv National Taras Shevchenko University
Department of Probability Theory, Statistics and Actuarial Mathematics, Professor

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Published
2016-12-07
How to Cite
Moklyachuk, M., & Sidei, M. (2016). Filtering Problem for Stationary Sequences with Missing Observations. Statistics, Optimization & Information Computing, 4(4), 308-325. https://doi.org/10.19139/soic.v4i4.241
Section
Research Articles