A refinement of Hoeffding's inequality

2013 ◽  
Vol 83 (5) ◽  
pp. 977-983 ◽  
Author(s):  
Steven G. From ◽  
Andrew W. Swift
Keyword(s):  
Hoeffding’S Inequality

scholarly journals New-type Hoeffding’s inequalities and application in tail bounds

2021 ◽  
Vol 5 (1) ◽  
pp. 248-261
Author(s):  
Pingyi Fan ◽  
Keyword(s):  
Information Processing ◽  
Random Variables ◽  
Order Moment ◽  
First Order ◽  
Hoeffding’S Inequalities ◽  
New Type ◽  
Hoeffding’S Inequality ◽  
Hoeffding Inequality ◽  
Moments Of Random Variables ◽  
Refined Version

It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz [<a href="#1">1</a>]. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding's inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding's inequality and its refined version by Hertz only considered the first order moment of random variables. In this paper, we present a new type of Hoeffding's inequalities, where the high order moments of random variables are taken into account. It can get some considerable improvements in the tail bounds evaluation compared with the known results. It is expected that the developed new type Hoeffding's inequalities could get more interesting applications in some related fields that use Hoeffding's results.

scholarly journals Distribution-free confidence intervals for measurement of effective bandwidth

2000 ◽  
Vol 37 (1) ◽  
pp. 224-235 ◽  
Author(s):  
László Györfi ◽  
András Rácz ◽  
Ken Duffy ◽  
John T. Lewis ◽  
Fergal Toomey
Keyword(s):  
Confidence Intervals ◽  
Interval Estimation ◽  
Effective Bandwidth ◽  
Distribution Free ◽  
Peak Rate ◽  
Estimation Procedures ◽  
Hoeffding’S Inequality ◽  
Traffic Source

Hoeffding's inequality can be used in conjunction with the declared parameters of a traffic source, such as its peak rate, to obtain confidence intervals for measurements of the traffic's effective bandwidth. We describe a variety of interval-estimation procedures based on this idea, designed to provide differing degrees of robustness against non-stationarity. We also discuss how to compute confidence intervals for the effective bandwidth of an aggregate of traffic sources.

A Note on Hoeffding's Inequality

1969 ◽  
Vol 64 (327) ◽  
pp. 907-912 ◽  
Author(s):  
O. Krafft ◽  
N. Schmitz
Keyword(s):  
Hoeffding’S Inequality
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