Multivariate Statistics Exercises and Solutions
The authors present tools and concepts of multivariate data analysis by means of exercises and their solutions. The first part is devoted to graphical techniques. The second part deals with multivariate random variables and presents the derivation of esti
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Wolfgang Hardle ä Zdenˇek Hl´avka
Multivariate Statistics: Exercises and Solutions
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Wolfgang Hardle .. Fakultatlnst Wirtschaftswissenschaftliche .. Statistik und Okonometrie .. Humboldt-Universitat zu Berlin, Berlin 1 Spandauer Str. Berlin 10178 Germany [email protected]
Zdenˇek Hl´ avka Dept. Mathematics Charles University in Prague Prague Czech Republic 83 Sokolovska Praha 8 186 75
Library of Congress Control Number: 2007929450
ISBN 978-0-387-70784-6
e-ISBN 978-0-387-73508-5
Printed on acid-free paper. c 2007 Springer Science+Business Media, LLC 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. 987654321 springer.com
F¨ ur meine Familie M´e rodinˇe
To our families
Preface
There can be no question, my dear Watson, of the value of exercise before breakfast. Sherlock Holmes in “The Adventure of Black Peter” The statistical analysis of multivariate data requires a variety of techniques that are entirely different from the analysis of one-dimensional data. The study of the joint distribution of many variables in high dimensions involves matrix techniques that are not part of standard curricula. The same is true for transformations and computer-intensive techniques, such as projection pursuit. The purpose of this book is to provide a set of exercises and solutions to help the student become familiar with the techniques necessary to analyze high-dimensional data. It is our belief that learning to apply multivariate statistics is like studying the elements of a criminological case. To become proficient, students must not simply follow a standardized procedure, they must compose with creativity the parts of the puzzle in order to see the big picture. We therefore refer to Sherlock Holmes and Dr. Watson citations as typical descriptors of the analysis. Puerile as such an exercise may seem, it sharpens the faculties of observation, and teaches one where to look and what to look for. Sherlock Holmes in “Study in Scarlet” Analytic creativity in applied statistics is interwoven with the ability to see and change the involved software algorithms. These are provided for the student via the links in the text. We recommend doing a small number of problems from this book a few times a week. And, it does not hurt to redo an exercise, even one that was mastered long ago. We have implemented in these links software quantlets from XploRe and R
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