Minimax-robust estimation problems for sequences with periodically stationary increments observed with noise

M. P. Moklyachuk; M. M. Luz

doi:10.17721/1812-5409.2020/3.7

Authors

M. P. Moklyachuk Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-6173-0280
M. M. Luz BNP Paribas Cardif, Kyiv, Ukraine https://orcid.org/0000-0002-8260-1584

DOI:

https://doi.org/10.17721/1812-5409.2020/3.7

Abstract

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas that determine the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are specified.

Key words: periodically stationary increments, minimax-robust estimate, least favorable spectral density, minimax-robust spectral characteristics.

Pages of the article in the issue: 68 - 83

Language of the article: English

Author Biography

M. P. Moklyachuk, Taras Shevchenko National University of Kyiv

Професор кафедри теорії ймовірностей, статистики і актуарної математики

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