Bounds for the uniform deviation of empirical measures

Luc Devroye

Journal of Multivariate Analysis, 1982, vol. 12, issue 1, 72-79

Abstract: If X1,...,Xn are independent identically distributed Rd-valued random vectors with probability measure [mu] and empirical probability measure [mu]n, and if is a subset of the Borel sets on Rd, then we show that P{supA[set membership, variant][mu]n(A)-[mu](A)>=[var epsilon]}

Keywords: Random; vector; empirical; measure; probability; inequality; uniform; consistency (search for similar items in EconPapers)
Date: 1982
References: Add references at CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(82)90083-5
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:jmvana:v:12:y:1982:i:1:p:72-79

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

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().