Applied Multivariate Statistical Analysis

This is probably the best applied statistics book I have ever read. It is not one of the "for dummies" book, it does use some linear algebra and requires some knowledge of elementary statistics, but at the same time it is very clear and understandable. I think this is the only reasonable approach - whatever you are told, you cannot understand statistics if you are not prepared - you can't run before you learn to walk. If you buy a "statistics for dummies" you will only waste your money - you will learn a few names of statistical methods (and possibly what to click in your favourite stats program) but you will not be able to use them. The authors start with a few examples, then lay out the formalism, and then use it in introducing various methods and techniques. The level of generality is not very high and you can read the book without the knowledge of, say, modern integration theory, yet it is sufficient for all the APPLIED problems that the reader is likely to meet in his/her work. (If you want to publish papers in AMSTAT journals you will have to learn more) A potential strength of this book is the electronic version which you can download using the code given at the end of the book, but I haven't done this so far. I assume that if you travel a lot you can carry the book on your laptop instead of your backpack. I have downloaded Xplore and find it quite nice, however, my stats system of choice is R, so I used this instead. There are some minor problems: for example there are some typos (some of them quite serious) and the end of chapter problems are not challenging enough (most can be done by inspection or by plugging numbers into Xplore). Speaking of the problems, the authors say that there is a solution manual, but it does not seem possible to get hold of it in any way. Still, the problems are so simple, that no solutions manual seems necessary. All in all, I highly recommend this book. Both thumbs up! Cover......Page 1 Applied Multivariate Statistical Analysis......Page 3 Preface to the 2nd Edition......Page 5 Preface to the 1st Edition......Page 6 Contents......Page 8 Part I Descriptive Techniques......Page 12 1 Comparison of Batches......Page 13 1.1 Boxplots......Page 14 1.2 Histograms......Page 20 1.3 Kernel Densities......Page 23 1.4 Scatterplots......Page 27 1.5 Chernoff-Flury Faces......Page 30 1.6 Andrews’ Curves......Page 33 1.7 Parallel Coordinate Plots......Page 37 1.8 Boston Housing......Page 38 1.9 Exercises......Page 45 Part II Multivariate Random Variables......Page 48 2.1 Elementary Operations......Page 49 2.2 Spectral Decompositions......Page 54 2.3 Quadratic Forms......Page 55 2.4 Derivatives......Page 58 2.5 Partitioned Matrices......Page 59 2.6 Geometrical Aspects......Page 60 2.7 Exercises......Page 67 3.1 Covariance......Page 69 3.2 Correlation......Page 73 3.3 Summary Statistics......Page 78 3.4 Linear Model for Two Variables......Page 81 3.5 Simple Analysis of Variance......Page 87 3.6 Multiple Linear Model......Page 91 3.7 Boston Housing......Page 95 3.8 Exercises......Page 98 4.1 Distribution and Density Function......Page 100 4.2 Moments and Characteristic Functions......Page 105 4.3 Transformations......Page 113 4.4 The Multinormal Distribution......Page 115 4.5 Sampling Distributions and Limit Theorems......Page 118 4.6 Heavy-Tailed Distributions......Page 125 4.7 Copulae......Page 139 4.8 Bootstrap......Page 148 4.9 Exercises......Page 151 5.1 Elementary Properties of the Multinormal......Page 154 5.2 The Wishart Distribution......Page 160 5.3 Hotelling’s T2-Distribution......Page 161 5.4 Spherical and Elliptical Distributions......Page 163 5.5 Exercises......Page 165 6.1 The Likelihood Function......Page 168 6.2 The Cramer-Rao Lower Bound......Page 172 6.3 Exercises......Page 175 7.1 Likelihood Ratio Test......Page 177 7.2 Linear Hypothesis......Page 185 7.3 Boston Housing......Page 200 7.4 Exercises......Page 202 Part III Multivariate Techniques......Page 206 8.1 The Geometric Point of View......Page 207 8.2 Fitting the p-dimensional Point Cloud......Page 209 8.3 Fitting the n-dimensional Point Cloud......Page 212 8.4 Relations between Subspaces......Page 213 8.5 Practical Computation......Page 215 8.6 Exercises......Page 217 9.1 Standardized Linear Combination......Page 219 9.2 Principal Components in Practice......Page 223 9.3 Interpretation of the PCs......Page 226 9.4 Asymptotic Properties of the PCs......Page 230 9.5 Normalized Principal Components Analysis......Page 232 9.6 Principal Components as a Factorial Method......Page 233 9.7 Common Principal Components......Page 238 9.8 Boston Housing......Page 241 9.9 More Examples......Page 243 9.10 Exercises......Page 251 10.1 The Orthogonal Factor Model......Page 254 10.2 Estimation of the Factor Model......Page 260 10.3 Factor Scores and Strategies......Page 267 10.4 Boston Housing......Page 268 10.5 Exercises......Page 272 11.1 The Problem......Page 274 11.2 The Proximity between Objects......Page 275 11.3 Cluster Algorithms......Page 279 11.4 Boston Housing......Page 287 11.5 Exercises......Page 288 12.1 Allocation Rules for Known Distributions......Page 292 12.2 Discrimination Rules in Practice......Page 298 12.3 Boston Housing......Page 303 12.4 Exercises......Page 304 13.1 Motivation......Page 307 13.2 Chi-square Decomposition......Page 309 13.3 Correspondence Analysis in Practice......Page 312 13.4 Exercises......Page 320 14.1 Most Interesting Linear Combination......Page 322 14.2 Canonical Correlation in Practice......Page 326 14.3 Exercises......Page 331 15.1 The Problem......Page 332 15.2 Metric Multidimensional Scaling......Page 337 15.3 Nonmetric Multidimensional Scaling......Page 340 15.4 Exercises......Page 347 16.1 Introduction......Page 348 16.2 Design of Data Generation......Page 350 16.3 Estimation of Preference Orderings......Page 352 16.4 Exercises......Page 358 17.1 Portfolio Choice......Page 360 17.2 Efficient Portfolio......Page 361 17.3 Efficient Portfolios in Practice......Page 366 17.4 The Capital Pricing Model (CAPM)......Page 368 17.5 Exercises......Page 369 18.1 Simplicial Depth......Page 371 18.2 Projection Pursuit......Page 375 18.3 Sliced Inverse Regression......Page 379 18.4 Support Vector Machines......Page 385 18.5 Classification and Regression Trees......Page 401 18.6 Boston Housing......Page 417 18.7 Exercises......Page 418 Part IV Appendix......Page 421 Samples......Page 422 Empirical Moments......Page 423 Distributions......Page 424 B.2 Swiss Bank Notes......Page 425 B.3 Car Data......Page 428 B.5 U.S. Companies Data......Page 430 B.7 Car Marks......Page 432 B.9 Journaux Data......Page 433 B.10 U.S. Crime Data......Page 434 B.11 Plasma Data......Page 435 B.12 WAIS Data......Page 436 B.13 ANOVA Data......Page 437 B.14 Timebudget Data......Page 438 B.15 Geopol Data......Page 439 B.16 U.S. Health Data......Page 441 B.17 Vocabulary Data......Page 442 B.18 Athletic Records Data......Page 443 B.20 Annual Population Data......Page 445 B.21 Bankruptcy Data......Page 446 Bibliography......Page 448 Index......Page 452 Most of the observable phenomena in the empirical sciences are of a multivariate nature.In financial studies, assets in stock markets are observed simultaneously and their joint development is analyzed to better understand general tendencies and to track indices. In medicine recorded observations of subjects in different locations are the basis of reliable diagnoses and medication. In quantitative marketing consumer preferences are collected in order to construct models of consumer behavior. The underlying theoretical structure of these and many other quantitative studies of applied sciences is multivariate. Focussing on applications this book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis. In this second edition a wider scope of methods and applications of multivariate statistical analysis is introduced. All quantlets have been translated into the R and Matlab language and are made available online. 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 devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents from a theoretical point of view distributions, estimators and tests for various practical situations. The last part covers multivariate techniques and introduces the reader into the wide basket of tools for multivariate data analysis. The text presents a wide range of examples and 228 exercises. "A state of the art presentation of the tools and concepts of multivariate data analysis with a strong focus on applications. The first part is devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents distributions, estimators and tests for various practical situations. The last part covers multivariate techniques and introduces the reader into the wide variety of tools for multivariate data analysis."--Jacket