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

Iosif Pinelis
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Abstract

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 ¶(S_n>x) \leq c¶(Z>x) for all x in \R is between two explicitly defined absolute constants c_1 and c_2 such that c_1<c_2 \approx 1.01c_1.

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Iosif Pinelis. 2006-05-12. Toward the best constant factor for the Rademacher-Gaussian tail comparison. https://arxiv.org/abs/math/0605340

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