Indexing metadata

Cram'er Type Moderate deviations for the Maximum of Self-normalized Sums


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Cram'er Type Moderate deviations for the Maximum of Self-normalized Sums
 
2. Creator Author's name, affiliation, country Zhishui Hu; USTC
 
2. Creator Author's name, affiliation, country Qi-Man Shao; HKUST
 
2. Creator Author's name, affiliation, country Qiying Wang; University of Sydney
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Large deviation, moderate deviation, self-normalized maximal sum
 
3. Subject Subject classification 60F10, 62E20
 
4. Description Abstract Let $\{ X, X_i , i \geq 1\}$ be i.i.d. random variables, $S_k$ be the partial sum and $V_n^2 = \sum_{1\leq i\leq n} X_i^2$. Assume that $E(X)=0$ and $E(X^4) < \infty$. In this paper we discuss the moderate deviations of the maximum of the self-normalized sums. In particular, we prove that $P(\max_{1 \leq k \leq n} S_k \geq x V_n) / (1- \Phi(x)) \to 2$ uniformly in $x \in [0, o(n^{1/6}))$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Z. Hu is partially supported by NSFC(No.10801122) and RFDP(No.200803581009); Q.M. Shao is partially supported by Hong Kong RGC 602206 and 602608; Q. Wang is partially supported by an ARC discovery project
 
7. Date (YYYY-MM-DD) 2009-05-31
 
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/663
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-663
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.