Estimating Averages of Order Statistics of Bivariate Functions

Lechner, Richard; Passenbrunner, Markus; Prochno, Joscha

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.

Citation

Lechner, R., Passenbrunner, M., & Prochno, J. (2017). Estimating Averages of Order Statistics of Bivariate Functions. Journal of theoretical probability, 30(4), 1445-1470. https://doi.org/10.1007/s10959-016-0702-8

• Journal Article Type: Article
• Acceptance Date: Aug 27, 2015
• Online Publication Date: Jul 9, 2016
• Publication Date: Dec 1, 2017
• Deposit Date: Jun 29, 2018
• 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
• DOI: https://doi.org/10.1007/s10959-016-0702-8
• Keywords: Order statistic; Orlicz space; Embedding
• Public URL: https://hull-repository.worktribe.com/output/900384
• Publisher URL: https://link.springer.com/article/10.1007%2Fs10959-016-0702-8