Multivariate Statistics.pdf

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Preface to the Second Edition

Preface to the First Edition

Contents

Symbols and Notation

Basics

Characteristics of Distribution

Moments

Samples

Empirical Moments

Distributions

Mathematical Abbreviations

Some Terminology

Part I Descriptive Techniques

1 Comparison of Batches

Part II Multivariate Random Variables

2 A Short Excursion into Matrix Algebra

3 Moving to Higher Dimensions

4 Multivariate Distributions

5 Theory of the Multinormal

6 Theory of Estimation

7 Hypothesis Testing

Part III Multivariate Techniques

8 Regression Models

Linear Regression

Logistic Regression

9 Variable Selection

10 Decomposition of Data Matrices by Factors

Representation of the p-Dimensional Data Cloud

Representation of the n-Dimensional Data Cloud

Duality Relations

11 Principal Component Analysis

12 Factor Analysis

Factor Analysis Model

Estimation of the Factor Model

Rotation

Strategy for Factor Analysis

13 Cluster Analysis

Agglomerative Algorithm

Intercluster Distance

Dendrogram

χ2 Distance

Euclidean Distance

Comparison

14 Discriminant Analysis

Maximum Likelihood Discriminant Rule

Bayes Discriminant Rule

Fisher's Linear Discrimination Function

15 Correspondence Analysis

16 Canonical Correlation Analysis

17 Multidimensional Scaling

Nonmetric Solution

18 Conjoint Measurement Analysis

Design of Data Generation

Estimation of Preferences

Nonmetric Solution

19 Applications in Finance

Efficient Portfolios

Capital Asset Pricing Model

20 Highly Interactive, Computationally Intensive Techniques

Simplicial Depth

Exploratory Projection Pursuit

Sliced Inverse Regression

SIR Algorithm

SIR II Algorithm

CART

Support Vector Machines

A Data Sets

A.1 Athletic Records Data

A.2 Bank Notes Data

A.3 Bankruptcy Data

A.4 Car Data

A.5 Car Marks

A.6 Classic Blue Pullover Data

A.7 Fertilizer Data

A.8 French Baccalauréat Frequencies

A.9 French Food Data

A.10 Geopol Data

A.11 German Annual Population Data

A.12 Journals Data

A.13 NYSE Returns Data

A.14 Plasma Data

A.15 Time Budget Data

A.16 Unemployment Data

A.17 U.S. Companies Data

A.18 U.S. Crime Data

A.19 U.S. Health Data

A.20 Vocabulary Data

A.21 WAIS Data

References

Index

Wolfgang Karl Härdle Zdeněk Hlávka Multivariate Statistics Exercises and Solutions Second Edition QUANTLETS

Multivariate Statistics

Wolfgang Karl HRardle • Zdenˇek Hlávka Multivariate Statistics Exercises and Solutions Second Edition 123

Wolfgang Karl HRardle C.A.S.E. Centre f. Appl. Stat. & Econ. School of Business and Economics Humboldt-Universität zu Berlin Berlin, Germany Zdenˇek Hlávka Charles University in Prague Faculty of Mathematics and Physics Department of Statistics Czech Republic The quantlet codes in Matlab or R may be downloaded from www.quantlet.com or via a link on http://springer.com/978-3-642-36004-6 ISBN 978-3-642-36004-6 DOI 10.1007/978-3-642-36005-3 ISBN 978-3-642-36005-3 (eBook) Library of Congress Control Number: 2015941507 Springer Heidelberg New York Dordrecht London © Springer-Verlag Berlin Heidelberg 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microﬁlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer-Verlag GmbH Berlin Heidelberg (www.springer.com) is part of Springer Science+Business Media

Für meine Familie Mé rodinˇe To our families

Preface to the Second Edition I have always had an idea that I would have made a highly efﬁcient criminal. This is the chance of my lifetime in that direction. See here! This is a ﬁrst-class, up-to-date burgling kit, with nickel-plated Jimmy, diamond-tipped glass-cutter, adaptable keys, and every modern improvement which the march of civilization demands. Sherlock Holmes in “The Adventure of Charles Augustus Milverton” The statistical science has seen new paradigms and more complex and richer data sets. These include data on human genomics, social networks, huge climate and weather data, and, of course, high frequency ﬁnancial and economic data. The statistical community has reacted to these challenges by developing modern mathematical tools and by advancing computational techniques, e.g., through fresher Quantlets and better hardware and software platforms. As a consequence, the book Härdle, W. and Simar, L. (2015) Applied Multivariate Statistical Analysis, 4th ed. Springer Verlag had to be adjusted and partly beefed up with more easy access tools and ﬁgures. An extra chapter on regression models with variable selection was introduced and dimension reduction methods were discussed. These new elements had to be reﬂected in the exercises and solutions book as well. We have now all ﬁgures completely redesigned in the freely available software R (R Core Team, 2013) that implements the classical statistical interactive language S (Becker, Chambers, & Wilks, 1988; Chambers & Hastie, 1992). The R codes for the classical multivariate analysis in Chaps. 11–17 are mostly based on library MASS (Venables & Ripley, 2002). Throughout the book, some examples are implemented directly in the R programming language but we have also used functions from R libraries aplpack (Wolf, 2012), ca (Nenadic & Greenacre, 2007), car (Fox & Weisberg, 2011), depth (Genest, Masse, & Plante, 2012), dr (Weisberg, 2002), glmnet (Friedman, Hastie, & Tibshirani, 2010), hexbin (Carr, Lewin-Koh, & Maechler, 2011), kernlab (Karatzoglou, Smola, Hornik, & Zeileis, 2004), KernS- mooth (Wand, 2012), lasso2 (Lokhorst, Venables, Turlach, & Maechler, 2013), locpol (Cabrera, 2012), MASS (Venables & Ripley, 2002), mvpart (Therneau, Atkinson, Ripley, Oksanen, & Deáth, 2012), quadprog (Turlach & Weingessel, 2011), scatterplot3d (Ligges & Mächler, 2003), stats (R Core Team, 2013), tseries vii

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