Iryna Golichenko¹ and Mikhail Moklyachuk^2
1National Technical University of Ukraine ”Igor Sikorsky Kyiv Politechnic Institute”, Department of Mathematical Analysis and Probability Theory, Kyiv, Ukraine,
²Taras Shevchenko National University of Kyiv, Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv, Ukraine

Chapter DOI: https://doi.org/10.52305/ABFI3483

Part of the book: Stochastic Processes: Fundamentals and Emerging Applications

Abstract

We propose results of the investigation of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of periodically correlated stochastic sequences. Estimates are based on observations of sequences with additive noise. Formulas for computing the value of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of functionals are proposed in the case of spectral uncertainty, where the spectral densities are not exactly known while some sets of admissible spectral densities are specified.

Keywords: stationary sequence, mean square error, minimax-robust estimate, least
favourable spectral density, minimax spectral characteristics

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