High Dimensional Probability
What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example th
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Series Editors Thomas Liggett Charles Newman Loren Pitt
High Dimensional Probability Emst Eberlein Marjorie Hahn Michel Talagrand Editors
Springer Basel AG
Editors' addresses: Ernst Eberlein Institut für Mathematische Stochastik Universität Freiburg Eckerstraße 1 79104 Freiburg Germany
Marjorie Hahn Department of Mathematics Tufts University Medford, M A 02155 USA
Michel Talagrand Equipe d'analyse, Tour 46 Universite Paris VI 4, place Jussieu 75230 Paris Cedex 05 France 1991 Mathematics Subject Classification: 60B11, 60B12, 60G15
A CIP catalogue record for this book is availablefromthe Library of Congress, Washington D . C , USA Deutsche Bibliothek Cataloging-in-Publication Data High dimensional probability / Ernst Eberlein ... ed. - Basel; Boston ; Berlin : Birkhäuser, 1998 (Progress in probability ; Vol. 43) ISBN 978-3-0348-9790-7 ISBN 978-3-0348-8829-5 (eBook) DOI 10.1007/978-3-0348-8829-5
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 1998 Springer Basel AG Originally published by Birkhäuser Verlag Basel in 1998 Softcover reprint of the hardcover 1st edition 1998
Printed on acid-free paper produced from chlorine-free pulp. TCF oo ISBN 978-3-0348-9790-7
98765432 1
Contents
Introduction .............................................................
vii
Miguel A. Arcones Weak Convergence of the Row Sums of a Triangular Array of Empirical Processes ..............................................
1
Amir Dembo, Qi-Man Shao Self-Normalized Large Deviations in Vector Spaces. . . . . . . . . . . . . . . . . . .
27
Richard M. Dudley Consistency of M -Estimators and One-Sided Bracketing
33
Thomas Dunker, Mikhail A. Lifshits, Werner Linde Small Deviation Probabilities of Sums of Independent Random Variables ..................................................
59
Uwe Einmahl, David M. Mason Strong Approximations to the Local Empirical Process
75
Peter Gaenssler, Daniel Rost, Klaus Ziegler On Random Measure Processes with Application to Smoothed Empirical Processes .................................................
93
Evarist Gine A Consequence for Random Polynomials of a Result of De La Perra and Montgomery-Smith.............. .......... .........
103
Marjorie G. Hahn, Gang Zhang Distinctions Between the Regular and Empirical Central Limit Theorems for Exchangeable Random Variables........ ......................... 111 Bernard Heinkel Laws of Large Numbers and Continuity of Processes
145
JyJrgen Hoffmann-JyJrgensen Convergence in Law of Random Elements and Random Sets
151
Vladimir I. Koltchinskii Asymptotics of Spectral Projections of Some Random Matrices Approximating Integral Operators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
191
Michel Ledoux A Short Proof of the
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