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

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

2006-05-12

arxiv.org/abs/math/0605340v1

ESAIM Probab. Stat. 11 (2007), 412--426

Mathematics

Probability

16 pages, 1 figure

Scientific paper

Let S_n:=a_1\vp_1+...+a_n\vp_n, where \vp_1,...,\vp_n are independent Rademacher random variables (r.v.'s) and a_1,...,a_n are any real numbers such that a_1^2+...+a_n^2=1. Let Z be a standard normal r.v. It is proved that the best constant factor c in inequality \P(S_n>x) \leq c\P(Z>x) for all x in \R is between two explicitly defined absolute constants c_1 and c_2 such that c_1

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