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High Dimensional Probability VI

Part of the Progress in Probability Book Series (volume 66)

Editors: Houdré, Christian; Mason, David M.; Rosiński, Jan; Wellner, Jon A.

DOI: 10.1007/978-3-0348-0490-5

ISBN: 978-3-0348-0489-9

Publisher: Springer Basel - Springer Journals

Apr 1, 2013

1 - 10 of 21 Chapters

LitStream

Bracketing Entropy of High Dimensional Distributions

Gao, Fuchang

Pages: 3 –17

[Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{F}_{d}$$...
LitStream

Slepian’s Inequality, Modularity and Integral Orderings

Hoffmann-Jørgensen, J.

Pages: 19 –53

[Slepian’s inequality comes in many variants under different sets of regularity conditions. Unfortunately, some of these variants are wrong and other variants are imposing to strong regularity conditions. The first part of this paper contains a unified version of Slepian’s inequality under...
LitStream

A More General Maximal Bernstein-type Inequality

Kevei, Péter; Mason, David M.

Pages: 55 –62

[We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.]
LitStream

Maximal Inequalities for Centered Norms of Sums of Independent Random Vectors

Latała, Rafał

Pages: 63 –71

[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...
LitStream

A Probabilistic Inequality Related to Negative Definite Functions

Lifshits, Mikhail; Schilling, René L.; Tyurin, Ilya

Pages: 73 –80

[We prove that for any pair of i.i.d. random vectors X,Y in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Optimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities

Pinelis, Iosif

Pages: 81 –93

[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}...
LitStream

Strong Log-concavity is Preserved by Convolution

Wellner, Jon A.

Pages: 95 –102

[We review and formulate results concerning strong-log-concavity in both discrete and continuous settings. Although four different proofs of preservation of strong log-concavity are known in the discrete setting (where strong log-concavity is known as “ultra-log-concavity”), preservation of...
LitStream

On Some Gaussian Concentration Inequality for Non-Lipschitz Functions

Wolff, Paweł

Pages: 103 –110

[A concentration inequality for functions of a pair of Gaussian random vectors is established. Instead of the usual Lipschitz condition some boundedness of second-order derivatives is assumed. This result can be viewed as an extension of a well-known tail estimate for Gaussian random bi-linear...
LitStream

Rates of Convergence in the Strong Invariance Principle for Non-adapted Sequences Application to Ergodic Automorphisms of the Torus

Dedecker, Jérôme; Merlevède, Florence; Pène, Françoise

Pages: 113 –138

[In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus \documentclass[12pt]{minimal} \usepackage{amsmath}...
LitStream

On the Rate of Convergence to the Semi-circular Law

Götze, Friedrich; Tikhomirov, Alexandre

Pages: 139 –165

[Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}...

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