More on the nonuniform Berry--Esseen bound

2013/02/03 by Iosif Pinelis, Pinelis, Iosif
Chemistry · Mathematics · #60E15 #62E17 #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Spectral Theory in Mathematical Physics #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1302.0516

openalex publication_date 2013/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Certain smoothing inequalities were proposed in the recent paper posted on arXiv at arxiv:1301.2828 in order to lessen the very large gap between the best correctly established upper and lower bounds on the constant factor in the nonuniform Berry-Esseen bound. As an illustration of the possible uses of those inequalities, a quick proof of Nagaev's classical nonuniform bound was given there. Here we describe another, apparently more effective class of smoothing inequalities, and give a yet quicker and simpler proof of Nagaev's result.

Citations

• On the absolute constants in the Berry-Esseen type inequalities for identically distributed summands
• New estimates of the convergence rate in the Lyapunov theorem

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• Improved nonuniform Berry--Esseen-type bounds
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