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Estimating Averages of Order Statistics of Bivariate Functions

Author

Listed:
  • Richard Lechner

    (Johannes Kepler University Linz)

  • Markus Passenbrunner

    (Johannes Kepler University Linz)

  • Joscha Prochno

    (University of Hull)

Abstract

We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, uniform estimates for the expected value of averages of order statistics of sequences of independent random variables in terms of Orlicz norms are obtained. In the case where the bivariate functions are matrices, we provide a “minimal” probability space which allows us to C-embed certain Orlicz spaces $$\ell _M^n$$ ℓ M n into $$\ell _1^{cn^3}$$ ℓ 1 c n 3 , with $$c,C>0$$ c , C > 0 being absolute constants.

Suggested Citation

  • Richard Lechner & Markus Passenbrunner & Joscha Prochno, 2017. "Estimating Averages of Order Statistics of Bivariate Functions," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1445-1470, December.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:4:d:10.1007_s10959-016-0702-8
    DOI: 10.1007/s10959-016-0702-8
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