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Variance Minimization and Random Variables with Constant Sum

In: Distributions With Given Marginals and Statistical Modelling

Author

Listed:
  • Ludger Rüschendorf

    (University of Freiburg, Institut für Mathematische Stochastik)

  • Ludger Uckelmann

    (University of Freiburg, Institut für Mathematische Stochastik)

Abstract

Abstract Motivated by the problem of variance minimization and the method of antithetic variates we consider the problem of construction of random variables with given marginals and constant sum. In the case of one dimensional symmetric, unimodal distributions we give a simple general construction. An alternative more complicated construction had been given previously by Knott and Smith (1998). In the multivariate case we consider the corresponding problem for affine transforms of products, elliptically contoured distributions, α-symmetric distributions and α-Cauchy distributions.

Suggested Citation

  • Ludger Rüschendorf & Ludger Uckelmann, 2002. "Variance Minimization and Random Variables with Constant Sum," Springer Books, in: Carles M. Cuadras & Josep Fortiana & José A. Rodriguez-Lallena (ed.), Distributions With Given Marginals and Statistical Modelling, pages 211-222, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0061-0_22
    DOI: 10.1007/978-94-017-0061-0_22
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