Sharpening of the Upper Bound of the Absolute Constant in the Berry–Esseen Inequality

2007/01/01 by Irina Shevtsova · 3 citations
Mathematics · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #Sharpening #Mathematics #Constant (computer programming) #Upper and lower bounds #Independent and identically distributed random variables #Absolute (philosophy) #Random variable #Inequality #Mathematical analysis #Statistics

paper · doi:10.1137/s0040585x97982591

openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06

Abstract

The upper bound of the absolute constant in the classical Berry–Esseen inequality for sums of independent identically distributed random variables with finite third moments is lowered to C\leqslant 0.7056.

Citations

• 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

Cited by

• On the Upper Bound for the Absolute Constant in the Berry–Esseen Inequality
• Coupling for Ornstein–Uhlenbeck processes with jumps
• Berry–Esseen theorem [wikipedia]