Abstract
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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Móri, T.F., Székely, GJ. Representations by uncorrelated random variables. Math. Meth. Stat. 26, 149–153 (2017). https://doi.org/10.3103/S1066530717020041
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DOI: https://doi.org/10.3103/S1066530717020041