Generalizations of maximal inequalities to arbitrary selection rules

Jiantao Jiao, Yanjun Han and Tsachy Weissman

Statistics & Probability Letters, 2018, vol. 137, issue C, 19-25

Abstract: We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of n jointly distributed random variables. We control the expectation of a randomly selected random variable from n jointly distributed random variables, and present bounds that are at least as tight as the classical maximal inequalities, and much tighter when the distribution of selection index is near deterministic. A new family of information theoretic measures was introduced in the process, which may be of independent interest.

Keywords: Entropy; Maximal inequality; Orlicz function; Convex duality; Generalized Holder’s inequality (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016771521830004X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:137:y:2018:i:c:p:19-25

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2018.01.002

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().