On the observation closest to the origin

L. de Haan and S. I. Resnick

Stochastic Processes and their Applications, 1981, vol. 11, issue 3, 301-308

Abstract: Out of n i.i.d. random vectors in d let X*n be the one closest to the origin. We show that X*n has a nondegenerate limit distribution if and only if the common probability distribution satisfies a condition of multidimensional regular variation. The result is then applied to a problem of density estimation.

Keywords: Multidimensional; regular; variation; destiny; estimation (search for similar items in EconPapers)
Date: 1981
References: Add references at CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(81)90032-6
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:spapps:v:11:y:1981:i:3:p:301-308

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

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().