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Optimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities

  • Iosif PinelisEmail author
Conference paper
Part of the Progress in Probability book series (PRPR, volume 66)

Abstract

For any nonnegative Borel-measurable function f such that \(f(x)\;=\;0\) if and only if \(x\;=\;0\), the best constant c f in the inequality \(Ef(X\;-\;E\;X)\leqslant c_f E\;f(X)\) for all random variables X with a finite mean is obtained. Properties of the constant c f in the case when \(f\;=\;|\cdot|^p\) for \(p>0\) are studied. Applications to concentration of measure in the form of Rosenthal-type bounds on the moments of separately Lipschitz functions on product spaces are given.

Keywords

Probability inequalities Rosenthal-type inequalities sums of independent random variables martingales concentration of measure separately Lipschitz functions product spaces 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesMichigan Technological UniversityHoughtonUSA

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