ESAIM: P&S, August 2007, Vol. 11, pp. 412-426
DOI: 10.1051/ps:2007027

Toward the best constant factor for the Rademacher-Gaussian tail comparison

Iosif Pinelis

Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931 USA; ipinelis@mtu.edu

(Received June 7, 2006. Revised November 2, 2006. Published online 17 August 2007.)

Abstract
It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants c₁ and c₂ such that c₂1.01 c₁. A discussion of relative merits of this result versus limit theorems is given.

Mathematics Subject Classification. 60E15, 62G10, 62G15, 60G50, 62G35

Key words: Probability inequalities, Rademacher random variables, sums of independent random variables, Student's test, self-normalized sums.


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