Domains of Semi-Stable Attraction of Nonnormal Semi-Stable Laws

H. P. Scheffler

Journal of Multivariate Analysis, 1994, vol. 51, issue 2, 432-444

Abstract: A sequence of independent, identically distributed random vectors X1, X2, ... is said to belong to the -normed domain of semi-stable attraction of a random vector Y if there exist diagonal matrices An, constant vectors bn and a sequence (kn)n of natural numbers with kn [upwards double arrow] [infinity] and kn+1/kn --> c >= 1 such that An(X1 + · · · + Xkn) + bn converges in distribution to Y. The limit law Y is then called semi-stable. We present a simple, necessary, and sufficient condition for the existence of such An, bn, and kn in the case where Y has no normal component. Furthermore we prove some moment conditions for random vectors belonging to the -normed domain of semi-stable attraction of Y.

Date: 1994
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(84)71071-2
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:51:y:1994:i:2:p:432-444

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 ().