Applied Multivariate Statistical Analysis

Wolfgang Härdle, Leopold Simar3540030794, 978-3-540-03079-9, 978-3-540-72243-4

Table of contents :
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