Optimal re-centering bounds, with applications to Rosenthal-type concentration of measure inequalities

Details Optimal re-centering bounds, with applications to Rosenthal-type concentration of measure inequalities Optimal re-centering bounds, with applications to Rosenthal-type concentration of measure inequalities

2011-11-10

arxiv.org/abs/1111.2622v1

Mathematics

Probability

Scientific paper

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 E f(X-E X) \leq 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=|.|^p 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.

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