General Bahr-Esseen inequalities and their applications

Abstract

Abstract We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent q > p $q>p$ for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence.

Keywords

• Bahr-Esseen inequality
• exponential inequality
• Rosenthal inequality
• strong law of large numbers
• complete convergence
• rate of convergence