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Estimating Averages of Order Statistics of Bivariate Functions

Lechner, Richard; Passenbrunner, Markus; Prochno, Joscha

Authors

Richard Lechner

Markus Passenbrunner

Joscha Prochno



Abstract

© 2016, Springer Science+Business Media New York. 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 ℓMn into ℓ1cn3, with c, C> 0 being absolute constants.

Journal Article Type Article
Publication Date Dec 1, 2017
Journal Journal of Theoretical Probability
Print ISSN 0894-9840
Electronic ISSN 1572-9230
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 30
Issue 4
Pages 1445-1470
APA6 Citation Lechner, R., Passenbrunner, M., & Prochno, J. (2017). Estimating Averages of Order Statistics of Bivariate Functions. Journal of theoretical probability, 30(4), 1445-1470. doi:10.1007/s10959-016-0702-8
DOI https://doi.org/10.1007/s10959-016-0702-8
Keywords Order statistic; Orlicz space; Embedding
Publisher URL https://link.springer.com/article/10.1007%2Fs10959-016-0702-8
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