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An asymptotically Gaussian bound on the Rademacher tails


 
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1. Title Title of document An asymptotically Gaussian bound on the Rademacher tails
 
2. Creator Author's name, affiliation, country Iosif Pinelis; Michigan Technological University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) probability inequalities; large deviations; Rade\-macher random variables; sums of independent random variables; Student's test; self-normalized sums; Esscher--Cram\'er tilt transform; generalized moments; Tchebycheff--Markov systems
 
3. Subject Subject classification Primary: 60E15. Secondary: 60F10; 62G10; 62G15; 60G50; 62G35
 
4. Description Abstract An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal distribution, thus affirming a longstanding conjecture by Efron. Applications to sums of general centered uniformly bounded independent random variables and to the Student test are presented.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Supported in part by NSF grant DMS-0805946 and NSA grant H98230-12-1-0237
 
7. Date (YYYY-MM-DD) 2012-05-15
 
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/2026
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2026
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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