Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations

  • Iryna Golichenko Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine ``Igor Sikorsky Kyiv Politechnic Institute''
  • Mikhail Moklyachuk Kyiv National Taras Shevchenko University
Keywords: Periodically correlated sequence, optimal linear estimate, mean square error, least favourable spectral density matrix, minimax spectral characteristic

Abstract

The problem of mean square optimal estimation of linear functionals which depend on the unknown values of a periodically correlated stochastic sequence is considered. The estimates are based on observations of the sequence with a noise. Formulas for calculation the mean square errors and the spectral characteristics of the optimal estimates of functionals are derived in the case of spectral certainty, where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, where spectral densities of the sequences are not exactly known while some classes of admissible spectral densities are specified.

Author Biography

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

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Published
2020-02-20
How to Cite
Golichenko, I., & Moklyachuk, M. (2020). Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations. Statistics, Optimization & Information Computing, 8(2), 631-654. https://doi.org/10.19139/soic-2310-5070-458
Section
Research Articles