Geodesic
Efficient measurement of higher-order statistics of stochastic processes
Kybernetika, Tome 54 (2018) no. 5, pp. 865-887 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14736/kyb-2018-5-0865
Classification : 15B05, 15B51, 60G10, 60G15, 93E24
Keywords: covariance matrix; higher-order statistics; adaptive; nonlinear 
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     title = {Efficient measurement of higher-order statistics of stochastic processes},
     journal = {Kybernetika},
     pages = {865--887},
     year = {2018},
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     doi = {10.14736/kyb-2018-5-0865},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-5-0865/}
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Magiera, Wladyslaw; Libal, Urszula; Wielgus, Agnieszka. Efficient measurement of higher-order statistics of stochastic processes. Kybernetika, Tome 54 (2018) no. 5, pp. 865-887. doi: 10.14736/kyb-2018-5-0865

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