ECP Reading Tools

Concentration inequalities for order statistics

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Concentration inequalities for order statistics
2.	Creator	Author's name, affiliation, country	Stéphane Vincent Boucheron; Université Paris-Diderot; France
2.	Creator	Author's name, affiliation, country	Maud Thomas; Université Paris-Diderot; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	concentration inequalities;entropy method;order statistics
3.	Subject	Subject classification	60E15;60F10;60G70;62G30;62G32
4.	Description	Abstract	This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. When the sampling distribution belongs to a maximum domain of attraction, these bounds are checked to be asymptotically tight. When the sampling distribution has a non decreasing hazard rate, we derive an exponential Efron-Stein inequality for order statistics, that is  an inequality connecting the logarithmic moment generating function of order statistics with exponential moments of Efron-Stein (jackknife) estimates of variance. This connection is used to derive variance and tail bounds for order statistics of Gaussian samples that are not within the scope of the Gaussian concentration inequality. Proofs are elementary and combine Rényi's representation of order statistics with the entropy approach to concentration of measure popularized by M. Ledoux.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2012-11-01
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/2210
10.	Identifier	Digital Object Identifier	10.1214/ECP.v17-2210
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.