Interpolation Problem for Multidimensional Stationary Processes with Missing Observations

  • Mikhail Moklyachuk Kyiv National Taras Shevchenko University
  • Oleksandr Masyutka Department of Mathematics and Theoretical Radiophysics, Taras Shevchenko National University of Kyiv,Ukraine
  • Maria Sidei Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv,Ukraine
DOI: https://doi.org/10.19139/soic.v7i1.430
Keywords: Stationary process, optimal estimate, mean square error, minimax-robust estimate, least favorable spectral density, minimax spectral characteristic

Abstract

The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic processis considered.Estimates are based on observations of the process with an additive stationary stochastic noise process at points which do not belong to some finite intervals of a real line. The problem is investigated in the case of spectral certainty, where the spectral densities of the processes are exactly known. Formulas for calculating the mean-square errors and spectral characteristics of the optimal linear estimates of functionals are proposed under the condition of spectral certainty. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities of the processes are not known exactly while some sets of admissible spectral densities of the processes are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special sets of admissible spectral densities.

Author Biography

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

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Published
2019-01-07
How to Cite
Moklyachuk, M., Masyutka, O., & Sidei, M. (2019). Interpolation Problem for Multidimensional Stationary Processes with Missing Observations. Statistics, Optimization & Information Computing, 7(1), 118-132. https://doi.org/10.19139/soic.v7i1.430
Issue
Vol 7 No 1 (2019)
Section
Research Articles
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