Estimating Averages of Order Statistics of Bivariate Functions

Richard Lechner (), Markus Passenbrunner () and Joscha Prochno ()
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Richard Lechner: Johannes Kepler University Linz
Markus Passenbrunner: Johannes Kepler University Linz
Joscha Prochno: University of Hull

Journal of Theoretical Probability, 2017, vol. 30, issue 4, 1445-1470

Abstract: 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.

Keywords: Order statistic; Orlicz space; Embedding; 62G30; 46B07; 46B45 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0702-8

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