Toward the best constant factor for the Rademacher-Gaussian tail comparison
Department of Mathematical Sciences,
Michigan Technological University,
Houghton, Michigan 49931 USA; email@example.com
Revised: 2 November 2006
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.
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.
© EDP Sciences, SMAI, 2007