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Toward the best constant factor for 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 c1 and c2 such that c2≈1.01 c1. 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.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 412 - 426
Copyright
© EDP Sciences, SMAI, 2007

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