Applied Multivariate Statistical Analysis
Most of the observable phenomena in the empirical sciences are of multivariate nature. This book presents the tools and concepts of multivariate data analysis with a strong focus on applications. The text is devided into three parts. The first part is dev
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Wolfgang HardIe • Leopold Simar
Applied Multivariate Statistical Analysis
~ Springer
Wolfgang Hardie Humboldt-Universitat zu Berlin CASE - Center for Applied Statistics and Economics Institut fur Statistik und Okonometrie Spandauer StraBe 1 10178 Berlin, Germany e-mail: [email protected]
Leopold Simar Universite Catholique Louvain Inst. Statistique voie du Roman Payas 20 1348 Louvain-Ia-Neuve, Belgium e-mail: [email protected] Cover art: Detail of "Portrait of the Franciscan monk Luca Pacioli, humanist and mathematician (1445-1517)"by Jacopo de Barbari,Museo di Capodimonte, Naples, Italy
This book is also available as e-book on www.i-xplore.de . Use the licence code at the end of the book to download the e-book. CataIoging-in-Publication Data applied lOr A catalog record lOr this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 978-3-540-03079-9 DOI 10.1007/978-3-662-05802-2
ISBN 978-3-662-05802-2 (eBook)
Mathematics Subject Classification (2000): 62Hl 0, 62H 12, 62H15, 62H17 ,62H20, 62H25, 62H30, 62F25 This work is subject to copyright An rights are reserved, whether the whole or part of the material is concerned, specificany the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH . Violations are liable for prosecution under the German Copyright Law. @Springer-VerlagBerlinHeidelberg 2003 Originally published by Springer-Verlag Berlin Hcidelberg New York in 2003
The use of general descriptive names, registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: design&production GmbH,Heidelberg Typesetting by the author using a MD'book macro package Printed on acid-free paper
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Contents
Descriptive Techniques 1 Comparison of Batches 1.1
Boxplots ..
11 13
14
1.2 Histograms
22
1.3 Kernel Densities .
25
1.4 Scatterplots ...
30
1.5 Chernoff-Flury Faces
34
1.6 Andrews' Curves ..
39
1.7 Parallel Coordinates Plots
42
1.8 Boston Housing
44
1.9 Exercises . . . .
52
Multivariate Random Variables
55
2 A Short Excursion into Matrix Algebra
57
II
2.1
Elementary Operations .
57
2.2
Spectral Decompositions
63
2.3
Quadratic Forms
65
2.4
Derivatives. . . .
68
2.5
Partitioned Matrices
68
Contents
2 2.6 Geometrical Aspects
71
2.7 Exercises . . . . . . .
79
3 Moving to Higher Dimensions
81
3.1 Covariance .
82
