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Decomposition of high-order statistics

Abstract : ANOVA analysis is a very common numerical technique for computing a hierarchy of most important input parameters for a given output when variations are computed in terms of variance. This second central moment can not be retained as an universal criterion for ranking some variables, since a non-gaussian output could require higher order (more than second) statistics for a complete description and analysis. In this work, we illustrate how third and fourth-order statistic moments, \textit{i.e.} skewness and kurtosis, respectively, can be decomposed. It is shown that this decomposition is correlated to a polynomial chaos expansion, permitting to easily compute each term. Then, new sensitivity indices are proposed basing on the computation of the kurtosis. An analytical example is provided with the explicit computation of the variance and the skewness. Some test-cases are introduced showing the importance of ranking the kurtosis too.
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https://hal.inria.fr/hal-00766853
Contributor : Pietro Marco Congedo <>
Submitted on : Wednesday, December 19, 2012 - 10:41:08 AM
Last modification on : Friday, February 26, 2021 - 11:20:02 AM
Long-term archiving on: : Wednesday, March 20, 2013 - 11:32:01 AM

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  • HAL Id : hal-00766853, version 1

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Remi Abgrall, Pietro Marco Congedo, Gianluca Geraci, Gianluca Iaccarino. Decomposition of high-order statistics. [Research Report] RR-8193, INRIA. 2012. ⟨hal-00766853⟩

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