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| Titel |
Detecting spatial patterns with the cumulant function – Part 1: The theory |
| VerfasserIn |
A. Bernacchia, P. Naveau |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 15, no. 1 ; Nr. 15, no. 1 (2008-02-19), S.159-167 |
| Datensatznummer |
250012562
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| Publikation (Nr.) |
 copernicus.org/npg-15-159-2008.pdf |
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| Zusammenfassung |
In climate studies,
detecting spatial patterns
that largely deviate from the sample mean
still remains a statistical challenge. Although a Principal Component
Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)
decomposition, is often applied for this purpose, it provides meaningful results only if the underlying multivariate
distribution is Gaussian.
Indeed, PCA is based on optimizing second order moments, and the covariance matrix captures the full dependence
structure of multivariate Gaussian vectors. Whenever the application at hand can not satisfy this
normality hypothesis (e.g. precipitation data), alternatives and/or
improvements to PCA have to be developed and studied.
To go beyond this second order statistics constraint, that limits the
applicability of the PCA, we take advantage of the cumulant function that can
produce higher order moments information. The cumulant function, well-known
in the statistical literature, allows us to propose a new, simple and fast
procedure to identify spatial patterns for non-Gaussian data. Our algorithm
consists in maximizing the cumulant function. Three families of multivariate
random vectors, for which explicit computations are obtained, are implemented
to illustrate our approach. In addition, we show that our algorithm
corresponds to selecting the directions along which projected data display
the largest spread over the marginal probability density tails. |
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