A central limit theorem for generalized multilinear forms

Peter de Jong

Journal of Multivariate Analysis, 1990, vol. 34, issue 2, 275-289

Abstract: Let X1, ..., Xn be independent random variables and define for each finite subset I [subset of] {1, ..., n} the [sigma]-algebra = [sigma]{Xi : i [epsilon] I}. In this paper -measurable random variables WI are considered, subject to the centering condition E(WI [short parallel] ) = 0 a.s. unless I [subset of] J. A central limit theorem is proven for d-homogeneous sums W(n) = [Sigma][short parallel]I[short parallel] = dWI, with var W(n) = 1, where the summation extends over all (nd) subsets I [subset of] {1, ..., n} of size [short parallel]I[short parallel] = d, under the condition that the normed fourth moment of W(n) tends to 3. Under some extra conditions the condition is also necessary.

Keywords: martingales; d-homogeneous; sums; Hoeffding; decomposition; central; limit; theorem (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(90)90040-O
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:34:y:1990:i:2:p:275-289

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 ().