Applied Multivariate Statistical Analysis

by Hardle, Wolfgang; Simar, Leopold

• ISBN13: 9783540722434
• ISBN10: 3540722432
• Edition: 2nd
• Format: Paperback
• Copyright: 2007-10-04
• Publisher: Springer Verlag

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
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