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.
Mathematics Subject Classification (2010). Primary 60E15; Secondary 46B09.
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Pinelis, I. (2013). Optimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities. In: Houdré, C., Mason, D., Rosiński, J., Wellner, J. (eds) High Dimensional Probability VI. Progress in Probability, vol 66. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0490-5_6
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DOI: https://doi.org/10.1007/978-3-0348-0490-5_6
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