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An asymptotically Gaussian bound on the Rademacher tails

   
@article{EJP2026,
	author = {Iosif Pinelis},
	title = {An asymptotically Gaussian bound on the Rademacher tails},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {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},
	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.},
	pages = {no. 35, 1-22},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-2026},    
        url = {http://ejp.ejpecp.org/article/view/2026}}