Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

Request Permissions   Purchase Content 
 

 

Minimax-robust filtering problem for stochastic sequences with stationary increments


Authors: M. M. Luz and M. P. Moklyachuk
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
Journal: Theor. Probability and Math. Statist. 89 (2014), 127-142
MSC (2010): Primary 60G10, 60G25, 60G35; Secondary 62M20, 93E10, 93E11
DOI: https://doi.org/10.1090/S0094-9000-2015-00940-6
Published electronically: January 26, 2015
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The problem of optimal estimation is considered for the linear functional

$\displaystyle A {\xi }=\sum _{k=0}^{\infty }a (k)\xi (-k),$

which depends on unknown values of a stochastic sequence $ \xi (k)$ with stationary $ n$-th order increments from observations of the sequence $ \xi (k)+\eta (k)$ for $ k=0,-1,-2,\dots $. Formulas suitable for calculating the mean-square error and spectral characteristic of the optimal linear estimate of the above functional are derived under the condition of the spectral definiteness, that is in the case where the spectral densities of the sequences $ \xi (k)$ and $ \eta (k)$ are exactly known. The minimax (robust) method of estimation is applied in the case where spectral densities are not known exactly but sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed for some special sets of admissible spectral densities.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G10, 60G25, 60G35, 62M20, 93E10, 93E11

Retrieve articles in all journals with MSC (2010): 60G10, 60G25, 60G35, 62M20, 93E10, 93E11


Additional Information

M. M. Luz
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine
Email: maksim_luz@ukr.net

M. P. Moklyachuk
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine
Email: mmp@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2015-00940-6
Keywords: Sequences with stationary increments, robust estimate, mean-square error, least favorable spectral density, minimax spectral characteristic
Received by editor(s): November 27, 2012
Published electronically: January 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society