Optimal re-centering bounds, with applications to Rosenthal-type concentration of measure inequalities
Probability
2017-01-17 v1 Statistics Theory
Statistics Theory
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 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.
Keywords
Cite
@article{arxiv.1111.2622,
title = {Optimal re-centering bounds, with applications to Rosenthal-type concentration of measure inequalities},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1111.2622},
year = {2017}
}