A central limit theorem for generalized multilinear forms
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.Download Info
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic Info
Article provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 34 (1990)
Issue (Month): 2 (August)
Pages: 275-289
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Order Information:
Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
Web: https://shop.elsevier.com/order?id=622892&ref=622892_01_ooc_1&version=01
Related research
Keywords: martingales d-homogeneous sums Hoeffding decomposition central limit theorem;References
No references listed on IDEASYou can help add them by filling out this form.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Gao, Jiti & Hong, Yongmiao, 2007. "Central limit theorems for weighted quadratic forms of dependent processes with applications in specification testing," MPRA Paper 11977, University Library of Munich, Germany, revised Dec 2007.
- Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:34:y:1990:i:2:p:275-289For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.