Multivariate Nonparametric Methods with R An approach based on spati
This book offers a new, fairly efficient, and robust alternative to analyzing multivariate data. The analysis of data based on multivariate spatial signs and ranks proceeds very much as does a traditional multivariate analysis relying on the assumption of
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Hannu Oja
Multivariate Nonparametric Methods with R An Approach Based on Spatial Signs and Ranks
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Prof. Hannu Oja University of Tampere Tampere School of Public Health FIN-33014 Tampere Finland [email protected]
ISSN 0930-0325 ISBN 978-1-4419-0467-6 e-ISBN 978-1-4419-0468-3 DOI 10.1007/978-1-4419-0468-3 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010924740 c Springer Science+Business Media, LLC 2010 ° All 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, 233 Spring Street, New York, NY 10013, USA), 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my family.
Preface
This book introduces a new way to analyze multivariate data. The analysis of data based on multivariate spatial signs and ranks proceeds very much as does a traditional multivariate analysis relying on the assumption of multivariate normality: the L2 norm is just replaced by different L1 norms, observation vectors are replaced by their (standardized and centered) spatial signs and ranks, and so on. The methods are fairly efficient and robust, and no moment assumptions are needed. A unified theory starting with the simple one-sample location problem and proceeding through the several-sample location problems to the general multivariate linear regression model and finally to the analysis of cluster-dependent data is presented. The material is divided into 14 chapters. Chapter 1 serves as a short introduction to the general ideas and strategies followed in the book. Chapter 2 introduces and discusses different types of parametric, nonparametric, and semiparametric statistical models used to analyze the multivariate data. Chapter 3 provides general descriptive tools to describe the properties of multivariate distributions and multivariate datasets. Multivariate location and scatter functionals and statistics and their use is described in detail. Chapter 4 introduces the concepts of multivariate spatial sign, signed-rank, and rank, and shows their connection to certain L1 objective functions. Also sign and rank covariance matrices are discussed carefully. The first four chapters thus provide the necessary tools to understand the remaining part of the book. The one-sample location case is treated thoroughly in Chapters 5-8. The book then starts with th
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