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On a Multivariate Version of Bernstein's Inequality


 
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1. Title Title of document On a Multivariate Version of Bernstein's Inequality
 
2. Creator Author's name, affiliation, country Peter Major; Renyi Mathematical Institute of the Hungarian Academy of Sciences
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Bernstein inequality, (degenerate) U-statistics, Wiener--It^o integrals, diagram formula, moment estimates
 
3. Subject Subject classification Primary 60E15, 60F10, Secondary 60H99
 
4. Description Abstract We prove such a multivariate version of Bernstein's inequality about the tail distribution of degenerate $U$-statistics which is an improvement of some former results. This estimate will be compared with an analogous bound about the tail distribution of multiple Wiener-Ito integrals. Their comparison shows that our estimate is sharp. The proof is based on good estimates about high moments of degenerate $U$-statistics. They are obtained by means of a diagram formula which enables us to express the product of degenerate $U$-statistics as the sum of such expressions.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Hungarian OTKA Foundation Nr. K61052
 
7. Date (YYYY-MM-DD) 2007-08-02
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/430
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-430
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
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