Improved nonuniform Berry--Esseen-type bounds
Iosif Pinelis
TL;DR
This paper develops new nonuniform Berry--Esseen bounds for sums of independent variables, leveraging Chen--Shao concentration techniques within the Stein method framework to improve understanding of distributional approximations.
Contribution
It introduces novel nonuniform bounds for sums of independent variables, extending recent work on nonlinear statistics using advanced concentration and Stein method techniques.
Findings
New bounds improve accuracy of distributional approximations.
Bounds are applicable to sums of independent variables.
Method enhances existing Berry--Esseen-type inequalities.
Abstract
New nonuniform Berry--Esseen-type bounds for sums of independent random variables are obtained, motivated by recent studies concerning such bounds for nonlinear statistics. The proofs are based on the Chen--Shao concentration techniques within the framework of the Stein method.
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Taxonomy
TopicsGraph theory and applications · Mathematical Inequalities and Applications · Analytic Number Theory Research