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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Interpolation of periodically correlated stochastic sequences


Authors: I. I. Dubovets’ka, O. Yu. Masyutka and M. P. Moklyachuk
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 43-56
MSC (2010): Primary 60G10, 60G25, 60G35; Secondary 62M20, 93E10, 93E11
Published electronically: July 26, 2012
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Abstract: We study the problem of optimal estimation of a linear functional of unknown values of a periodically correlated random sequence from observed values of a sequence with an additive noise. Formulas for calculating the mean square error and spectral characteristic of the optimal linear estimate of a functional are established in the case where the spectral densities are known. The least favorable spectral densities and minimax spectral characteristic of the optimal linear estimate of a functional are found for some classes of admissible spectral densities.


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Additional Information

I. I. Dubovets’ka
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kyiv 03127, Ukraine
Email: idubovetska@gmail.com

O. Yu. Masyutka
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kyiv 03127, Ukraine

M. P. Moklyachuk
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kyiv 03127, Ukraine
Email: mmp@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00862-4
PII: S 0094-9000(2012)00862-4
Keywords: Periodically correlated sequence, robust estimate, mean square error, least favorable spectral density, minimax spectral characteristic
Received by editor(s): November 28, 2010
Published electronically: July 26, 2012
Article copyright: © Copyright 2012 American Mathematical Society