On estimation problem for continuous time stationary processes from observations in special sets of points

O. Yu. Masyutka; I. I. Golichenko; M. P. Moklyachuk

doi:10.17721/1812-5409.2022/1.2

Authors

O. Yu. Masyutka Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-7301-8813
I. I. Golichenko National Technical University of Ukraine ”Igor Sikorsky Kyiv Politechnic Institute”, Kyiv 03056 https://orcid.org/0000-0001-5639-8271
M. P. Moklyachuk Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-6173-0280

DOI:

https://doi.org/10.17721/1812-5409.2022/1.2

Keywords:

stationary stochastic process, minimax-robust estimate, least favorable spectral density, minimax-robust spectral characteristics

Abstract

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary process from observations of the process with missings is considered. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functionals are derived under the condition of spectral certainty, where the spectral density of the process is exactly known. The minimax (robust) method of estimation is applied in the case where the spectral density of the process is not known exactly while some sets of admissible spectral densities are given. Formulas that determine the least favourable spectral densities and the minimax spectral characteristics are derived for some special sets of admissible densities.

Pages of the article in the issue: 20 - 33

Language of the article: English

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