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 , where and are multidimensional stationary stochastic sequences. The estimation is based on observations of the sequence for . 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