# Applied Multivariate Statistical Analysis

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

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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Page vii - The book is divided into three main parts. The first part is devoted to graphical techniques describing the distributions of the variables involved.
Page 6 - Then, draw a line from each end of the box to the most remote point that is not an outlier.