Efficient measurement of higher-order statistics of stochastic processes

Wladyslaw Magiera; Urszula Libal; Agnieszka Wielgus

Kybernetika (2018)

  • Volume: 54, Issue: 5, page 865-887
  • ISSN: 0023-5954

Abstract

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This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance matrices), which are necessary taking in mind practical aspects of the nonlinear treatment of the least-squares estimation problem. The algorithms are examined for different higher-order and non-Gaussian processes (time-series) and an impact of signal properties on covariance matrices is analysed.

How to cite

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Magiera, Wladyslaw, Libal, Urszula, and Wielgus, Agnieszka. "Efficient measurement of higher-order statistics of stochastic processes." Kybernetika 54.5 (2018): 865-887. <http://eudml.org/doc/294182>.

@article{Magiera2018,
abstract = {This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance matrices), which are necessary taking in mind practical aspects of the nonlinear treatment of the least-squares estimation problem. The algorithms are examined for different higher-order and non-Gaussian processes (time-series) and an impact of signal properties on covariance matrices is analysed.},
author = {Magiera, Wladyslaw, Libal, Urszula, Wielgus, Agnieszka},
journal = {Kybernetika},
keywords = {covariance matrix; higher-order statistics; adaptive; nonlinear},
language = {eng},
number = {5},
pages = {865-887},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Efficient measurement of higher-order statistics of stochastic processes},
url = {http://eudml.org/doc/294182},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Magiera, Wladyslaw
AU - Libal, Urszula
AU - Wielgus, Agnieszka
TI - Efficient measurement of higher-order statistics of stochastic processes
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 5
SP - 865
EP - 887
AB - This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance matrices), which are necessary taking in mind practical aspects of the nonlinear treatment of the least-squares estimation problem. The algorithms are examined for different higher-order and non-Gaussian processes (time-series) and an impact of signal properties on covariance matrices is analysed.
LA - eng
KW - covariance matrix; higher-order statistics; adaptive; nonlinear
UR - http://eudml.org/doc/294182
ER -

References

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  9. Schur, I., 10.1007/978-3-0348-5483-2, Operator Theory: Advances and Applications 18, Springer-Verlag 1086. DOI10.1007/978-3-0348-5483-2
  10. Stellakis, H. M., Manolakos, E. M., 10.1002/(sici)1099-1115(199603)10:2/3<283::aid-acs351>3.3.co;2-2, Int. J. Adaptive Control Signal Process. 10 (1996), 283-302. DOI10.1002/(sici)1099-1115(199603)10:2/3<283::aid-acs351>3.3.co;2-2
  11. Wiener, N., Nonlinear Problems in Random Theory., MIT Press, 1958. MR0100912
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