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New nonuniform Berry--Esseen-type bounds for sums of independent random variables are obtained, motivated by recent studies concerning such bounds for nonlinear statistics.
Probability inequalities for the sum of independent random variables
G. Bennett · 1962
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Probability inequalities for sums of bounded random variables
W. Hoeffding · 1963
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Estimates of the remainder term in the central limit theorem
A. Bikelis · 1966
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Asymptotic expansions in the central limit theorem
L. V. Osipov · 1967
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Integral limit theorems with regard to large deviations when Cramér’s condition is not satisfied. I
A. V. Nagaev · 1969
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Integral limit theorems with regard to large deviations when Cramér’s condition is not satisfied. II
A. V. Nagaev · 1969
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The remainder terms of an asymptotic expansion of the distribution function of a sum of independent random variables
V. Pipiras · 1970
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Sums of independent random variables
V. V. Petrov · 1975
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A problem on large deviations in a space of trajectories
I. F. Pinelis · 1981
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Sharp exponential estimates for sums of independent random variables
I. F. Pinelis and S. A. Utev · 1989
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Optimum bounds for the distributions of martingales in Banach spaces
I. Pinelis · 1994
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Optimal tail comparison based on comparison of moments
I. Pinelis · 1998
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A non-uniform Berry-Esseen bound via Stein’s method
L. H. Y. Chen and Q.-M. Shao · 2001
Later among the works it cites.
On Hoeffding’s inequalities
V. Bentkus · 2004
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Stein’s method for normal approximation
L. H. Y. Chen and Q.-M. Shao · 2005
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Normal approximation for nonlinear statistics using a concentration inequality approach
L. H. Y. Chen and Q.-M. Shao · 2007
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Exact lower bounds on the exponential moments of Winsorized and truncated random variables
I. Pinelis · 2011
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I. Pinelis
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