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Toward the best constant factorfor the Rademacher-Gaussian tail comparison

Published online by Cambridge University Press:  17 August 2007

Iosif Pinelis
Iosif Pinelis*
Affiliation:
Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931 USA; ipinelis@mtu.edu
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Abstract

It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants c 1 and c 2 such that c 2 ≈1.01 c 1.A discussion of relative merits of this result versus limit theorems is given.

Keywords

Probability inequalitiesRademacher random variablessums of independent random variablesStudent's testself-normalized sums.

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