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High Dimensional Probability VIMaximal Inequalities for Centered Norms of Sums of Independent Random Vectors

High Dimensional Probability VI: Maximal Inequalities for Centered Norms of Sums of Independent... [Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ X_1,\,X_2 ,\,.\,.\,.\,,X_n $$ \end{document} be independent random variables and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ S_k = \sum\nolimits_{i = 1}^k {X_i } $$ \end{document} We show that for any constants ak\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{P}(\mathop \mathrm{max}\limits_{1\leq k \leq n} \|S_k |-{a_k}|>11{t})\leq 30 \mathop \mathrm{max}\limits_{1\leq k \leq n} \mathbb{P}(\|S_k | -{a_k}|>t).$$ \end{document}We also discuss similar inequalities for sums of Hilbert and Banach spacevalued random vectors.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

High Dimensional Probability VIMaximal Inequalities for Centered Norms of Sums of Independent Random Vectors

Part of the Progress in Probability Book Series (volume 66)
Editors: Houdré, Christian; Mason, David M.; Rosiński, Jan; Wellner, Jon A.
Latała, Rafał
High Dimensional Probability VI — Apr 1, 2013
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References (5)

Publisher
Springer Basel
Copyright
© Springer Basel 2013
ISBN
978-3-0348-0489-9
Pages
63 –71
DOI
10.1007/978-3-0348-0490-5_4
Publisher site
See Chapter on Publisher Site

Abstract

[Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ X_1,\,X_2 ,\,.\,.\,.\,,X_n $$ \end{document} be independent random variables and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ S_k = \sum\nolimits_{i = 1}^k {X_i } $$ \end{document} We show that for any constants ak\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{P}(\mathop \mathrm{max}\limits_{1\leq k \leq n} \|S_k |-{a_k}|>11{t})\leq 30 \mathop \mathrm{max}\limits_{1\leq k \leq n} \mathbb{P}(\|S_k | -{a_k}|>t).$$ \end{document}We also discuss similar inequalities for sums of Hilbert and Banach spacevalued random vectors.]

Published: Apr 1, 2013

Keywords: Sums of independent random variables; random vectors; maximal inequality

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