Threshold Results for U-Statistics of Dependent Binary Variables

Niels G. Becker () and Sergey Utev ()
Additional contact information
Niels G. Becker: Australian National University
Sergey Utev: Australian National University

Journal of Theoretical Probability, 2001, vol. 14, issue 1, 97-114

Abstract: Abstract Large sample results for certain U-statistics, and related statistics, of binary dependent random variables are studied. The class of U-statistics include partial sums and polynomials of partial sums of a sequence of random variables. A very wide range of limit results are found. The form of the limit result can depend substantially on the magnitude of the appropriate normalizing sequence for the sum. Unexpectedly, the nature of the limit result also depends significantly on whether the degree of the U-statistic is even or odd. It is shown that dependence is a major factor contributing to this result. The limit results are illustrated with reference to a simple dynamic sequence of binary variables and a reinforced random walk.

Keywords: U-statistics; dependent binary variables; threshold results (search for similar items in EconPapers)
Date: 2001
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1007821131604 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jotpro:v:14:y:2001:i:1:d:10.1023_a:1007821131604

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1007821131604

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().