Interpolation of periodically correlated stochastic sequences
Authors:
I. I. Dubovets’ka, O. Yu. Masyutka and M. P. Moklyachuk
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 84 (2012), 43-56
MSC (2010):
Primary 60G10, 60G25, 60G35; Secondary 62M20, 93E10, 93E11
DOI:
https://doi.org/10.1090/S0094-9000-2012-00862-4
Published electronically:
July 26, 2012
MathSciNet review:
2857415
Full-text PDF Free Access
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Additional Information
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.
References
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References
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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
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