Limit distributions of V- and U-statistics in terms of multiple stochastic Wiener-type integrals

Dietmar Ferger and Michael Scholz

Journal of Multivariate Analysis, 2011, vol. 102, issue 2, 306-314

Abstract: We describe the limit distribution of V- and U-statistics in a new fashion. In the case of V-statistics the limit variable is a multiple stochastic integral with respect to an abstract Brownian bridge GQ. This extends the pioneer work of Filippova (1961) [8]. In the case of U-statistics we obtain a linear combination of GQ-integrals with coefficients stemming from Hermite Polynomials. This is an alternative representation of the limit distribution as given by Dynkin and Mandelbaum (1983) [7] or Rubin and Vitale (1980) [13]. It is in total accordance with their results for product kernels.

Date: 2011
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00196-X
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:102:y:2011:i:2:p:306-314

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 ().