On the concentration phenomenon for [phi]-subgaussian random elements

Rita Giuliano Antonini, Tien-Chung Hu and Andrei Volodin

Statistics & Probability Letters, 2006, vol. 76, issue 5, 465-469

Abstract: We study the deviation probability P{[short parallel]X[short parallel]-E[short parallel]X[short parallel]>t} where X is a [phi]-subgaussian random element taking values in the Hilbert space l2 and [phi](x) is an N-function. It is shown that the order of this deviation is exp{-[phi]*(Ct)}, where C depends on the sum of [phi]-subgaussian standard of the coordinates of the random element X and [phi]*(x) is the Young-Fenchel transform of [phi](x). An application to the classically subgaussian random variables ([phi](x)=x2/2) is given.

Keywords: Concentration; of; measure; phenomenon; [phi]-Subgaussian; random; variables; N-function; Young-Fenchel; transform; Exponential; inequalities (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00326-3
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:76:y:2006:i:5:p:465-469

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

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 ().