Extrapolation Problem for Stationary Sequences with Missing Observations

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

Abstract

In this paper, we consider the  problem  of the mean square optimal estimation of linear functionals  which depend on unknown values of a stationary stochastic sequence based on observations of the sequence with a stationary noise. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functional 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 of the sequences 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 Biographies

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

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Published
2017-08-29
How to Cite
Moklyachuk, M., & Sidei, M. (2017). Extrapolation Problem for Stationary Sequences with Missing Observations. Statistics, Optimization & Information Computing, 5(3), 212-233. https://doi.org/10.19139/soic.v5i3.284
Section
Research Articles