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

DOI10.1051/ps:2007027zbMath1185.60017arXivmath/0605340OpenAlexW2118506245MaRDI QIDQ5429613

Iosif Pinelis

Publication date: 30 November 2007

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605340

zbMATH Keywords

sums of independent random variablesprobability inequalitiesself-normalized sumsstudent's testrademacher random variables

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Nonparametric robustness (62G35) Inequalities; stochastic orderings (60E15) Nonparametric tolerance and confidence regions (62G15) Sums of independent random variables; random walks (60G50)

Related Items (7)

Tail bounds for empirically standardized sums ⋮ Exact inequalities for sums of asymmetric random variables, with applications ⋮ An extension of the Hoeffding inequality to unbounded random variables ⋮ Bounds for tail probabilities of martingales using skewness and kurtosis ⋮ On the supremum of the tails of normalized sums of independent Rademacher random variables ⋮ A tight Gaussian bound for weighted sums of Rademacher random variables ⋮ Rademacher–Gaussian tail comparison for complex coefficients and related problems

Cites Work

• Extremal probabilistic problems and Hotelling's \(T^ 2\) test under a symmetry condition
• A probability inequality for linear combinations of bounded random variables
• An inequality for tail probabilities of martingales with differences bounded from one side
• A remark on Bernstein, Prokhorov, Bennett, Hoeffding, and Talagrand inequalities
• On Hoeffding's inequalities.
• On normal domination of (super)martingales
• Exact inequalities for sums of asymmetric random variables, with applications
• An Inequality of Optimal Order for the Tail Probabilities of the T Statistic Under Symmetry
• Binomial upper bounds on generalized moments and tail probabilities of (super)martingales with differences bounded from above
• Extremal problems in the maximal inequalities of Khintchine
• Student's t-Test Under Symmetry Conditions
• On Gaussian and Bernoulli covariance representations
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