Mathematical Methods of Statistics

, Volume 26, Issue 2, pp 149–153 | Cite as

Representations by uncorrelated random variables

  • T. F. Móri
  • G.-J. Székely


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.


uncorrelatedness Neyman-Pearson lemma Hermite polynomials Gaussian random variables 

2000 Mathematics Subject Classification

primary 62H20 secondary 62E10 


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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Dept. Probab. Theory and Statist.Eötvös Loránd Univ.BudapestHungary
  2. 2.Nat. Sci. FoundationArlingtonUSA
  3. 3.Rényi Inst. of Math., Hungarian Acad. Sci.BudapestHungary

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