A refinement of Hoeffding's inequality

Abstract

In this paper, we present a refinement of Hoeffding's inequality which is of closed form and which significantly improves on this inequality in many cases. Some numerical comparisons are also presented.

Keywords:

• Hoeffding's inequality
• arithmetic mean–geometric mean inequality
• moment-generating function

AMS Subject Classifications :

• 60E15
• 62E17

Acknowledgements

The authors thank the referee whose comments helped to improve this paper. In particular, the comments allowed us to generate a more streamlined proof of Theorem 1.3.