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.
Keywordsuncorrelatedness Neyman-Pearson lemma Hermite polynomials Gaussian random variables
2000 Mathematics Subject Classificationprimary 62H20 secondary 62E10
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- 5.E. L. Melnick and A. Tenenbein, Misspecifications of the Normal Distribution”, Amer. Statist. 36, 372–373 (1982).Google Scholar
- 8.H. Wackernagel, Multivariate Geostatistics: An Introduction with Applications, in Springer Science+ Business Media (Springer, Berlin, 2003), 3rd ed.Google Scholar