Multivariate Statistical Analysis A High-Dimensional Approach
In the last few decades the accumulation of large amounts of in formation in numerous applications. has stimtllated an increased in terest in multivariate analysis. Computer technologies allow one to use multi-dimensional and multi-parametric models suc
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THEORY AND DECISION LIBRARY General Editors: W. Leinfellner (Vienna) and G. Eberlein (Munich) Series A: Philosophy and Methodology of the Social Sciences Series B: Mathematical and Statistical Methods Series C: Game Theory, Mathematical Programming and Operations Research
SERIES B: MATHEMATICAL AND STATISTICAL METHODS VOLUME 41
Editor: H. J. Skala (Paderborn); Assistant Editor: M. Kraft (Paderborn); Editorial Board: J. Aczel (Waterloo, Ont.), G. Bamberg (Augsburg), H. Drygas (Kassel), W. Eichhorn (Karlsruhe), P. Fishburn (Murray Hill, N.J.), D. Fraser (Toronto), W. Janko (Vienna), P. de Jong (Vancouver), T. Kariya (Tokyo), M. Machina (La Jolla, Calif.), A. Rapoport (Toronto), M. Richter (Kaiserslautern), B. K. Sinha (Cattonsville, Md.), D. A. Sprott (Waterloo, Ont.), P. Suppes (Stanford, Calif.), H. Theil (St. Augustine, Fla.), E. Trillas (Madrid), L. A. Zadeh (Berkeley, Calif.).
Scope: The series focuses on the application of methods and ideas oflogic, mathematics and statistics to the social sciences. In particular, formal treatment of social phenomena, the analysis of decision making, information theory and problems of inference will be central themes of this part of the library. Besides theoretical results, empirical investigations and the testing of theoretical models of real world problems will be subjects of interest. In addition to emphasizing interdisciplinary communication, the series will seek to support the rapid dissemination of recent results.
MULTIVARIATE STATISTICAL ANALYSIS A High-Dimensional Approach
by
V. Serdobolskii Department of Applied Mathematics, Moscow Institute of Electronics and Mathematics, Moscow, Russia
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-5593-4 ISBN 978-94-015-9468-4 (eBook) DOI 10.1007/978-94-015-9468-4
Printed an acid-free paper
AII Rights Reserved © 2000 Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 2000 Softcover reprint ofthe hardcover lst edition 2000 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permis sion from the copyright owner.
CONTENTS
Preface
ix
Introduction Kolmogorov Asymptotics in Problems of Multivariate Analysis Spectral Theory of Large Covariance Matrices 1. Limit Formulas for Spectral Functions 2. Spectral Functions for Fixed Dimension and Sample Size 3. Method to Single out the Leading Terms Approximately Unim provable Essentially Multivariate Procedures
14
Chapter 1. Spectral Properties of Large Wishart Matrices
25
Wishart Distribution Limit Moments of Wishart Matrices Limit Formula for the Resolvent of Wishart Matrices
Chapter 2. Resolvents and Spectral Functions of Large Sample Covariance Matrices Spectral Functions of Random Gram Matrices Spectral Functions of Sample Covariance Matrices Limi
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