Applied Multivariate Statistical Analysis
by Hardle, Wolfgang; Simar, LeopoldEdition: 2nd
Format: Paperback
Pub. Date: 2007-10-04
Publisher(s): Springer Verlag
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Summary
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.
Author Biography
Leopold Simar is Professor of Statistics at The Univeriste Catholique de Louvain, Louvain-la-Neuve, Belgium where he is the Founder-Chairman of the Institute of Statistics. He is also Professor at The Facultes Universitaires Saint-Louis, Brussels, Belgium.
Table of Contents
| Preface to the 2nd Edition | p. v |
| Preface to the 1st Edition | p. vii |
| Descriptive Techniques | p. 1 |
| Comparison of Batches | p. 3 |
| Boxplots | p. 4 |
| Histograms | p. 10 |
| Kernel Densities | p. 13 |
| Scatterplots | p. 17 |
| Chernoff-Flury Faces | p. 21 |
| Andrews' Curves | p. 23 |
| Parallel Coordinate Plots | p. 27 |
| Boston Housing | p. 28 |
| Exercises | p. 35 |
| Multivariate Random Variables | p. 39 |
| A Short Excursion into Matrix Algebra | p. 41 |
| Elementary Operations | p. 41 |
| Spectral Decompositions | p. 40 |
| Quadratic Forms | p. 47 |
| Derivatives | p. 50 |
| Partitioned Matrices | p. 51 |
| Geometrical Aspects | p. 52 |
| Exercises | p. 59 |
| Moving to Higher Dimensions | p. 61 |
| Covariance | p. 61 |
| Correlation | p. 65 |
| Summary Statistics | p. 70 |
| Linear Model for Two Variables | p. 73 |
| Simple Analysis of Variance | p. 73 |
| Multiple Linear Model | p. 83 |
| Boston Housing | p. 87 |
| Exercises | p. 90 |
| Multivariate Distributions | p. 93 |
| Distribution and Density Function | p. 93 |
| Moments and Characteristic Functions | p. 98 |
| Transformations | p. 106 |
| The Multinomial Distribution | p. 108 |
| Sampling Distributions and Limit Theorems | p. 111 |
| Heavy-Tailed Distributions | p. 118 |
| Copulae | p. 132 |
| Bootstrap | p. 141 |
| Exercises | p. 144 |
| Theory of the Multinormal | p. 147 |
| Elementary Properties of the Multmormal | p. 147 |
| The Wishart Distribution | p. 153 |
| Hotelling's T2-Distribution | p. 154 |
| Spherical and Elliptical Distributions | p. 156 |
| Exorcises | p. 158 |
| Theory of Estimation | p. 161 |
| The Likelihood Function | p. 161 |
| Tim Cramer-Rao Lower Bound | p. 165 |
| Exercises | p. 168 |
| Hypothesis Testing | p. 171 |
| Likelihood Ratio Test | p. 171 |
| Linear Hypothesis | p. 179 |
| Boston Housing | p. 194 |
| Exercises | p. 196 |
| Multivariate Techniques | p. 201 |
| Decomposition of Data Matrices by Factors | p. 203 |
| The Geometric Point of View | p. 203 |
| Fitting the p-dimensional Point Cloud | p. 200 |
| Fitting the n-dimensional Point Cloud | p. 208 |
| Relations between Subspaces | p. 209 |
| Practical Computation | p. 211 |
| Exercises | p. 213 |
| Principal Components Analysis | p. 215 |
| Standardized Linear Combination | p. 215 |
| Principal Component Practice | p. 219 |
| Interpretation of the PCs | p. 222 |
| Asymptotic Properties of the: PCs | p. 226 |
| Normalized Principal Components Analysis | p. 228 |
| Principal Components us a Factorial Method | p. 229 |
| Common Principal Components | p. 234 |
| Boston Housing | p. 237 |
| More Examples | p. 239 |
| Exercises | p. 247 |
| Factor Analysis | p. 251 |
| The Orthogonal Factor Model | p. 251 |
| Estimation of the Factor Model | p. 257 |
| Factor Scores and Strategies | p. 264 |
| Boston Housing | p. 265 |
| Exercises | p. 269 |
| Cluster Analysis | p. 271 |
| The Problem | p. 271 |
| The Proximity between Objects | p. 272 |
| Cluster Algorithms | p. 270 |
| Boston Housing | p. 284 |
| Exercises | p. 285 |
| Discriminant Analysis | p. 289 |
| Allocation Rules for Known Distributions | p. 289 |
| Discrimination Rules in Practice | p. 295 |
| Boston Housing | p. 300 |
| Exercises | p. 301 |
| Correspondence Analysis | p. 305 |
| Motivation | p. 300 |
| Chi-square Decomposition | p. 307 |
| Correspondence Analysis in Practice | p. 310 |
| Exercises | p. 318 |
| Canonical Correlation Analysis | p. 321 |
| Most Interesting Linear Combination | p. 321 |
| Canonical Correlation in Practice | p. 325 |
| Exercises | p. 330 |
| Multidimensional Scaling | p. 331 |
| The Problem | p. 331 |
| Metric Multidimensional Scaling | p. 336 |
| Nonmetric Multidimensional Scaling | p. 339 |
| Exercises | p. 346 |
| Conjoint Measurement Analysis | p. 347 |
| Introduction | p. 347 |
| Design of Data Generation | p. 349 |
| Estimation of Preference Ordering | p. 351 |
| Exercises | p. 356 |
| Applications in Finance | p. 359 |
| Portfolio Choice | p. 359 |
| Efficient Portfolio | p. 360 |
| Efficient Portfolios in Practice | p. 365 |
| The Capital Pricing Model (CAPM) | p. 367 |
| Exercises | p. 368 |
| Computationally Intensive Techniques | p. 371 |
| Simplicial Depth | p. 371 |
| Projection Pursuit | p. 375 |
| Sliced Inverse Regression | p. 379 |
| Support. Vector Machines | p. 385 |
| Classification and Regression Trees | p. 401 |
| Boston Housing | p. 417 |
| Exercises | p. 418 |
| Appendix | p. 421 |
| Symbols and Notations | p. 423 |
| Data | p. 427 |
| Boston Housing Data | p. 427 |
| Swiss Bank Notes | p. 427 |
| Car Data | p. 430 |
| Classic Blue Pullovers Data | p. 432 |
| U.S. Companies Data | p. 432 |
| French Food Data | p. 434 |
| Car Marks | p. 434 |
| French Baccalauréat Frequencies | p. 435 |
| Journatux Data | p. 435 |
| U.S. Crime Data | p. 430 |
| Plasma Data | p. 437 |
| WAIS Data | p. 438 |
| ANOVA Data | p. 439 |
| Timebudget Data | p. 440 |
| Geopol Data | p. 441 |
| U.S. Health Data | p. 443 |
| Vocabulary Data | p. 444 |
| Athletic Records Data | p. 445 |
| Unemployment Data | p. 447 |
| Annual Population Data | p. 447 |
| Bankruptcy Data | p. 448 |
| Bibliography | p. 451 |
| Index | p. 455 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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