High Dimensional Probability II
High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gau
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Series Editors Thomas Liggett Charles Newman Loren Pitt
High Dimensional Probability II Evarist Gine David M. Mason Jon A. Wellner Editors
Springer-Science+Business Media, LLC
Evarist Gin6 Departments of Mathematics & Statistics University of Connecticut Storrs, CT 06269 USA
David M. Mason Department of Food and Resource Econ. University of Delaware Newark, DE 19717 USA
Jon A. Wellner Department of Statistics University of Washington Seattle, WA 98195 USA Library of Congress Cataloging-in-Publication Data High dimensional probability II/Evarist Gine\ David M . Mason, Jon A. Wellner, editors, p. cm. - (progress in probability ; 47) Includes bibliographical references. ISBN 978-1-4612-7111-6 ISBN 978-1-4612-1358-1 (eBook) DOI 10.1007/978-1-4612-1358-1 1. Probabilities-Congresses. 2. Linear topological spaces-Congresses. 3. Gaussian processes-Congresses. I. Gine\ Evarist, 1944- II. Mason, David M., 1946- III. Wellner, Jon A., 1945- IV. International Conference on High Dimensional Probability (2nd : 1999 : University of Washington) V. Series QA273.A1 H54 2000 519.2-dc21
00-058525
AMS Subject Classifications: 60B11,60B12,60E05,60E07,60E15,60F05,60F10,60F15,60F17, 60G15, 60G17, 60G40, 60G44, 60G50, 60H25, 60J25, 60J30, 60J60, 60J65, 62E17, 62E20, 62G07, 63G09, 62G20 Printed on acid-free paper. © 2000 Springer Science+Business Media New York Originally published by Birkhäuser Boston in 2000 Softcover reprint of the hardcover 1st edition 2000 A l l rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer-Science+Business Media, LLC, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be usedfreelyby anyone. ISBN 978-1-4612-7111-6
Reformatted from editors' files in lAlfeX by TfeXniques, Inc., Cambridge, M A .
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Contents
Preface ............................................................... ix 1. Inequalities ........................................................ 1 Moment Bounds for Self-Normalized Martingales Victor H. de la Pena, Michael J. Klass, and Tze Leung Lai . ............ 3 Exponential and Moment Inequalities for U-Statistics Evarist Gine, Rafal Latala, and Joel Zinn ............................. 13 A Multiplicative Inequality for Concentration Functions of n-Fold Convolutions Friedrich Gotze and Andrei Yu. Zaitsev ................................ 39 On Exact Maximal Khinchine Inequalities Iosif Pinelis .......................................................... 49 Strong Exponential Integrability of Martingales with Increments Bounded by
