Estimating averages of order statistics of bivariate functions

Richard Lechner; Markus Passenbrunner; Joscha Prochno

doi:10.1007/s10959-016-0702-8

Estimating averages of order statistics of bivariate functions

Richard Lechner, Markus Passenbrunner, Joscha Prochno

Department of Functional Analysis

Research output: Contribution to journal › Article › peer-review

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 ℓ^n_M into ℓ^{cn^3}_1 with c,C>0 being absolute constants.

Original language	English
Pages (from-to)	1445–1470
Number of pages	26
Journal	Journal of Theoretical Probability
Volume	30
Issue number	4
DOIs	https://doi.org/10.1007/s10959-016-0702-8
Publication status	Published - 2017

Fields of science

101002 Analysis

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.1007/s10959-016-0702-8

Cite this

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AU - Passenbrunner, Markus

AU - Prochno, Joscha

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AB - 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 ℓ^n_M into ℓ^{cn^3}_1 with c,C>0 being absolute constants.

U2 - 10.1007/s10959-016-0702-8

DO - 10.1007/s10959-016-0702-8

M3 - Article

SN - 1572-9230

VL - 30

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JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

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