Sharp large deviations for sums of bounded from above random variables

DOI10.1007/s11425-017-9144-9zbMath1382.60053OpenAlexW2751231266MaRDI QIDQ681925

Xiequan Fan

Publication date: 13 February 2018

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-017-9144-9

zbMATH Keywords

sums of independent random variablesTalagrand inequalityHoeffding inequalityCramér large deviationssharp large deviations

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Large deviations (60F10)

Related Items (4)

Cramér moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications ⋮ Self-normalized Cramér type moderate deviations for stationary sequences and applications ⋮ Cramér type moderate deviations for self-normalized \(\psi \)-mixing sequences ⋮ Cramér moderate deviations for a supercritical Galton-Watson process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hoeffding's inequality for supermartingales
• Berry-Esseen type estimates for large deviation probabilities
• Sharp large deviation results for sums of independent random variables
• On domination of tail probabilities of (super)martingales: explicit bounds
• A Cramér type large deviation result for Student's \(t\)-statistic
• Self-normalized Cramér-type large deviations for independent random variables.
• Large deviations for martingales via Cramér's method
• On Hoeffding's inequalities.
• The missing factor in Hoeffding's inequalities
• Cramér large deviation expansions for martingales under Bernstein's condition
• On the Bennett-Hoeffding inequality
• On Deviations of the Sample Mean
• Probability Inequalities for the Sum of Independent Random Variables
• Sharp Large Deviations for the Ornstein--Uhlenbeck Process
• Lower Bounds for Probabilities of Large Deviations of Sums of Independent Random Variables
• Probability Inequalities for Sums of Bounded Random Variables
• On Large and Superlarge Deviations of Sums of Independent Random Vectors Under Cramér's Condition. II
• Large Deviations for Sums of Independent Non Identically Distributed Random Variables
• Student's t-Test Under Symmetry Conditions
• A non-uniform Berry-Esseen bound via Stein's method

This page was built for publication: Sharp large deviations for sums of bounded from above random variables