Poisson and Gaussian approximation of weighted local empirical processes

John Einmahl

Stochastic Processes and their Applications, 1997, vol. 70, issue 1, 31-58

Abstract: We consider the local empirical process indexed by sets, a substantial generalization of the well-studied uniform tail empirical process. We show that the weak limit of weighted versions of this process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main theorems provide many new results as well as a unified approach to a number of asymptotic distributional results for weighted empirical processes, which up to now appeared to be isolated facts. Our results have applications in 'local' statistical procedures; we will, in particular, show their usefulness in multivariate extreme value theory.

Keywords: 60F05; 60F17; 62E20; 62G30; Extreme; value; theory; Local; and; tail; empirical; process; Weak; laws (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (27)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00055-0
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:70:y:1997:i:1:p:31-58

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 ().