# Extrapolation Problem for Multidimensional Stationary Sequences with Missing Observations

• Mikhail Moklyachuk Kyiv National Taras Shevchenko University
• Oleksandr Masyutka Department of Mathematics and Theoretical Radiophysics, Kyiv National Taras Shevchenko University, Ukraine
• Maria Sidei Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine
Keywords: Stationary sequence, mean square error, minimax-robust estimate, least favorable spectral density, minimax spectral characteristic

### Abstract

This paper focuses on the problem of the mean square optimal estimation of linear functionals which dependon the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of these quence with an additive stationary noise sequence. The aim of the paper is to develop methods of finding the optimal estimates of the functionals in the case of missing observations. The problem is investigated in the case of spectral certainty where the spectral densities of the sequences are exactly known. 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.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 of the optimal estimates of functionals 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
2019-01-07
How to Cite
Moklyachuk, M., Masyutka, O., & Sidei, M. (2019). Extrapolation Problem for Multidimensional Stationary Sequences with Missing Observations. Statistics, Optimization & Information Computing, 7(1), 97-117. https://doi.org/10.19139/soic.v7i1.527
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Section
Research Articles

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