Title: A Berry-Esséen Inequality without Higher Order Moments

Author(s): Ningning Wang and Ibrahim A. Ahmad
Issue: Volume 78 Series A Part 2 Year 2016
Pages: 180 -- 187
In this note, a generalized form of the celebrated Berry-Esséen inequality is developed assuming only second-order moments to exist in the case of independent but not identically distributed random variables. The result generalizes and unifies many well known and highly used forms of the Berry- Esséen inequality.
AMS (2000) subject classification . Primary: 60F05.
Keywords and phrases: Berry-Esséen inequality, Central limit theorem, Convergence rates.