Applied Multivariate Statistical Analysis

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Springer Science & Business Media, Aug 9, 2007 - Mathematics - 458 pages
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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.

 

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Chapter 8 dualität von row-space und column-space der datenmatrix

Contents

Comparison of Batches
3
11 Boxplots
4
12 Histograms
10
13 Kernel Densities
13
14 Scatterplots
17
15 ChernoffFlury Faces
20
16 Andrews Curves
23
17 Parallel Coordinate Plots
27
910 Exercises
247
Factor Analysis
250
102 Estimation of the Factor Model
257
103 Factor Scores and Strategies
264
104 Boston Housing
265
105 Exercises
269
Cluster Analysis
271
112 The Proximity between Objects
272

18 Boston Housing
28
19 Exercises
35
Multivariate Random Variables
38
A Short Excursion into Matrix Algebra
41
22 Spectral Decompositions
46
23 Quadratic Forms
47
24 Derivatives
50
25 Partitioned Matrices
51
26 Geometrical Aspects
52
27 Exercises
59
Moving to Higher Dimensions
61
32 Correlation
65
33 Summary Statistics
70
34 Linear Model for Two Variables
73
35 Simple Analysis of Variance
79
36 Multiple Linear Model
83
37 Boston Housing
87
38 Exercises
90
Multivariate Distributions
92
42 Moments and Characteristic Functions
98
43 Transformations
106
44 The Multinormal Distribution
108
45 Sampling Distributions and Limit Theorems
111
46 HeavyTailed Distributions
118
47 Copulae
132
48 Bootstrap
141
49 Exercises
144
Theory of the Multinormal
147
52 The Wishart Distribution
153
53 Hotellings T²Distribution
154
54 Spherical and Elliptical Distributions
156
55 Exercises
158
Theory of Estimation
161
62 The CramerRao Lower Bound
165
63 Exercises
168
Hypothesis Testing
171
72 Linear Hypothesis
179
73 Boston Housing
194
74 Exercises
196
Multivariate Techniques
200
Decomposition of Data Matrices by Factors
203
82 Fitting the pdimensional Point Cloud
205
83 Fitting the ndimensional Point Cloud
208
84 Relations between Subspaces
209
85 Practical Computation
211
86 Exercises
213
Principal Components Analysis
215
92 Principal Components in Practice
219
93 Interpretation of the PCs
222
94 Asymptotic Properties of the PCs
226
95 Normalized Principal Components Analysis
228
96 Principal Components as a Factorial Method
229
97 Common Principal Components
234
98 Boston Housing
237
99 More Examples
239
113 Cluster Algorithms
276
114 Boston Housing
284
115 Exercises
285
Discriminant Analysis
289
122 Discrimination Rules in Practice
295
123 Boston Housing
300
124 Exercises
301
Correspondence Analysis
305
132 Chisquare Decomposition
307
133 Correspondence Analysis in Practice
310
134 Exercises
318
Canonical Correlation Analysis
320
142 Canonical Correlation in Practice
325
143 Exercises
330
Multidimensional Scaling
331
152 Metric Multidimensional Scaling
336
153 Nonmetric Multidimensional Scaling
339
154 Exercises
346
Conjoint Measurement Analysis
347
162 Design of Data Generation
349
163 Estimation of Preference Orderings
351
164 Exercises
357
Applications in Finance
359
172 Efficient Portfolio
360
173 Efficient Portfolios in Practice
365
174 The Capital Pricing Model CAPM
367
175 Exercises
368
Computationally Intensive Techniques
371
182 Projection Pursuit
375
183 Sliced Inverse Regression
379
184 Support Vector Machines
385
185 Classification and Regression Trees
401
186 Boston Housing
417
187 Exercises
418
Appendix
421
Symbols and Notations
422
Data
427
B3 Car Data
430
B4 Classic Blue Pullovers Data
432
B6 French Food Data
434
B8 French Baccalauréat Frequencies
435
B10 US Crime Data
436
B11 Plasma Data
437
B12 WAIS Data
438
B13 ANOVA Data
439
B14 Timebudget Data
440
B15 Geopol Data
441
B16 US Health Data
443
B17 Vocabulary Data
444
B18 Athletic Records Data
445
B19 Unemployment Data
447
B21 Bankruptcy Data
448
Bibliography
450
Index
455
Copyright

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