On the Upper Bound for the Absolute Constant in the Berry–Esseen Inequality

2010/01/01 by V. Yu. Korolev, Irina Shevtsova · 2 citations
Mathematics · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Graph theory and applications #Mathematics #Constant (computer programming) #Absolute (philosophy) #Inequality #Independent and identically distributed random variables #Berry #Upper and lower bounds #Random variable #Mathematical analysis #Statistics #Computer science

paper · doi:10.1137/s0040585x97984449

openalex publication_date 2010/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

This paper describes the history of the search for unconditional and conditional upper bounds of the absolute constant in the Berry–Esseen inequality for sums of independent identically distributed random variables. Computational procedures are described. New estimates are presented from which it follows that the absolute constant in the classical Berry–Esseen inequality does not exceed 0.5129.

Citations

• Refinement of the upper bound of the constant in the central limit theorem
• Sharpening of the Upper Bound of the Absolute Constant in the Berry–Esseen Inequality
• An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality
• The accuracy of the Gaussian approximation to the sum of independent variates
• On the central limit theorem in the case of not equally distributed random variables
• On the central limit theorem
• A sharpening of the inequality of Berry-Esseen

Cited by

• Upper bounds on secret-key agreement over lossy thermal bosonic channels
• Berry–Esseen theorem [wikipedia]

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• On the nonuniform Berry--Esseen bound
• On the Berry-Esseen bound for the Student statistic
• Improved nonuniform Berry--Esseen-type bounds
• An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums