Representations by uncorrelated random variables

Representations by uncorrelated random variables

All multivariate random variables with finite variances are univariate functions of uncorrelated random variables and if the multivariate distribution is absolutely continuous then these univariate functions are piecewise linear. They can be independent of the correlations in the Gaussian case.

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Bibliographische Detailangaben
Veröffentlicht in:Mathematical methods of statistics 2017-04, Vol.26 (2), p.149-153
Hauptverfasser: Móri, T. F., Székely, G.-J.
Format: Artikel
Sprache:eng
Schlagworte:
Continuity (mathematics)
Mathematical analysis
Mathematics and Statistics
Normal distribution
Random variables
Statistical Theory and Methods
Statistics
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Beschreibung
Zusammenfassung:All multivariate random variables with finite variances are univariate functions of uncorrelated random variables and if the multivariate distribution is absolutely continuous then these univariate functions are piecewise linear. They can be independent of the correlations in the Gaussian case.
ISSN:1066-5307
1934-8045
DOI:10.3103/S1066530717020041