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Theory of Probability and Mathematical Statistics

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Interpolation of multidimensional stationary sequences


Authors: M. P. Moklyachuk and O. Yu. Masyutka
Translated by: M. P. Moklyachuk
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 125-133
MSC (2000): Primary 60G10; Secondary 60G35, 62M20, 93E10, 93E11
DOI: https://doi.org/10.1090/S0094-9000-07-00687-4
Published electronically: January 17, 2007
MathSciNet review: 2213847
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Abstract | References | Similar Articles | Additional Information

Abstract: The problem of optimal estimation is considered for the linear functional $ A_{N}\vec{\xi}=\sum_{j=0}^{N}\vec{a}(j)\vec {\xi }(j)$, where $ \{\vec{\xi}(j)\}$ and $ \{\vec{\eta}(j)\}$ are multidimensional stationary stochastic sequences. The estimation is based on observations of the sequence $ \vec {\xi} (j)+\vec {\eta} (j)$ for $ j \in Z\setminus {\left\{ {0,\dots, N} \right\}}$. We obtain formulas for calculating the mean-square error and spectral characteristic of the optimal estimate of the functional. The least favorable spectral densities and minimax spectral characteristics of the optimal estimates of the functional are found for some classes of spectral densities.


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Additional Information

M. P. Moklyachuk
Affiliation: Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, Kyiv National Taras Shevchenko University, Volodymyrs’ka Street 64, Kyiv 01033, Ukraine
Email: mmp@univ.kiev.ua

O. Yu. Masyutka
Affiliation: Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, Kyiv National Taras Shevchenko University, Volodymyrs’ka Street 64, Kyiv 01033, Ukraine

DOI: https://doi.org/10.1090/S0094-9000-07-00687-4
Keywords: Multidimensional stationary sequence, optimal linear estimate, mean-square error, spectral characteristic, least favorable spectral density, minimax-robust spectral characteristic
Received by editor(s): May 20, 2005
Published electronically: January 17, 2007
Dedicated: This paper is dedicated to our teacher Mykhaĭlo Ĭosypovych Yadrenko.
Article copyright: © Copyright 2007 American Mathematical Society

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