Bounding Probability of Small Deviation: A Fourth Moment Approach

@article{He2010BoundingPO,
  title={Bounding Probability of Small Deviation: A Fourth Moment Approach},
  author={Simai He and Jiawei Zhang and Shuzhong Zhang},
  journal={Math. Oper. Res.},
  year={2010},
  volume={35},
  pages={208-232}
}
In this paper we study the problem of upper bounding the probability that a random variable is above its expected value by a small amount (relative to the expected value), by means of the second and the fourth (central) moments of the random variable. In this particular context, many classical inequalities yield only trivial bounds. We obtain tight upper bounds by studying the primal-dual moments-generating conic optimization problems. As an application, we demonstrate that given the new… Expand
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References

SHOWING 1-10 OF 21 REFERENCES
The fourth moment method
  • B. Berger
  • Mathematics, Computer Science
  • SODA '91
  • 1991
Optimal Inequalities in Probability Theory: A Convex Optimization Approach
A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions
  • I. Popescu
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 2005
Approximation and Intractability Results for the Maximum Cut Problem and its Variants
Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis
The Probabilistic Method
On the Relation Between Option and Stock Prices: A Convex Optimization Approach
Lectures on modern convex optimization - analysis, algorithms, and engineering applications
...
1
2
3
...