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), 125133
MSC (2000):
Primary 60G10; Secondary 60G35, 62M20, 93E10, 93E11
Published electronically:
January 17, 2007
MathSciNet review:
2213847
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: The problem of optimal estimation is considered for the linear functional , where and are multidimensional stationary stochastic sequences. The estimation is based on observations of the sequence for . We obtain formulas for calculating the meansquare 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:
http://dx.doi.org/10.1090/S0094900007006874
PII:
S 00949000(07)006874
Keywords:
Multidimensional stationary sequence,
optimal linear estimate,
meansquare error,
spectral characteristic,
least favorable spectral density,
minimaxrobust 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
