# High Dimensional Probability VIOptimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities

High Dimensional Probability VI: Optimal Re-centering Bounds, with Applications to Rosenthal-type... [For any nonnegative Borel-measurable function f such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f(x)\;=\;0$$ \end{document} if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x\;=\;0$$ \end{document}, the best constant cf in the inequality \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$Ef(X\;-\;E\;X)\leqslant c_f E\;f(X)$$ \end{document} for all random variables X with a finite mean is obtained. Properties of the constant cf in the case when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f\;=\;|\cdot|^p$$ \end{document} for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$p>0$$ \end{document} 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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# High Dimensional Probability VIOptimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities

Part of the Progress in Probability Book Series (volume 66)
Editors: Houdré, Christian; Mason, David M.; Rosiński, Jan; Wellner, Jon A.
12 pages

/lp/springer-journals/high-dimensional-probability-vi-optimal-re-centering-bounds-with-lwhSZL0416

# References (33)

Publisher
Springer Basel
ISBN
978-3-0348-0489-9
Pages
81 –93
DOI
10.1007/978-3-0348-0490-5_6
Publisher site
See Chapter on Publisher Site

### Abstract

[For any nonnegative Borel-measurable function f such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f(x)\;=\;0$$ \end{document} if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x\;=\;0$$ \end{document}, the best constant cf in the inequality \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$Ef(X\;-\;E\;X)\leqslant c_f E\;f(X)$$ \end{document} for all random variables X with a finite mean is obtained. Properties of the constant cf in the case when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f\;=\;|\cdot|^p$$ \end{document} for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$p>0$$ \end{document} 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.]

Published: Apr 1, 2013

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