Mathematical Methods of Statistics

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

Representations by uncorrelated random variables

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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.

Keywords

uncorrelatedness Neyman-Pearson lemma Hermite polynomials Gaussian random variables 

2000 Mathematics Subject Classification

primary 62H20 secondary 62E10 

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References

  1. 1.
    D. R. Cox and N. Reid, “Parameter Orthogonality and Approximate Conditional Inference”, J. R. Statist. Soc. Ser. B. Statist. Methodol. 49, 1–39 (1987).MathSciNetMATHGoogle Scholar
  2. 2.
    A. K. Gupta, T. F. Móri, and G. J. Székely, “How to Transform Random Variables into Uncorrelated Ones”, Appl. Math. Lett. 13, 31–33 (2000).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    A. M. Kagan, Yu. V. Linnik, and C. R. Rao, Characterization Problems in Mathematical Statistics. (Wiley, New York, 1973).MATHGoogle Scholar
  4. 4.
    E. L. Lehmann, Testing Statistical Hypotheses (Wiley, New York, 1986), 2nd ed.CrossRefMATHGoogle Scholar
  5. 5.
    E. L. Melnick and A. Tenenbein, Misspecifications of the Normal Distribution”, Amer. Statist. 36, 372–373 (1982).Google Scholar
  6. 6.
    T. F. Móri, “Essential Correlatedness and Almost Independence”, Statist. Probab. Lett. 15, 169–172 (1992).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    J. C. Oxtoby, Measure and Category (Springer, New York, 1980), 2nd ed.CrossRefMATHGoogle Scholar
  8. 8.
    H. Wackernagel, Multivariate Geostatistics: An Introduction with Applications, in Springer Science+ Business Media (Springer, Berlin, 2003), 3rd ed.Google Scholar

Copyright information

© 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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