Applied multivariate statistical analysis:
Now in its sixth edition, this textbook presents the tools and concepts used in multivariate data analysis in a style accessible for non-mathematicians and practitioners. Each chapter features hands-on exercises that showcase applications across various fields of multivariate data analysis. These ex...
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Hauptverfasser: | , , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cham, Switzerland
Springer
[2024]
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Ausgabe: | Sixth edition |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Zusammenfassung: | Now in its sixth edition, this textbook presents the tools and concepts used in multivariate data analysis in a style accessible for non-mathematicians and practitioners. Each chapter features hands-on exercises that showcase applications across various fields of multivariate data analysis. These exercises utilize high-dimensional to ultra-high-dimensional data, reflecting real-world challenges in big data analysis.For this new edition, the book has been updated and revised and now includes new chapters on modern machine learning techniques for dimension reduction and data visualization, namely locally linear embedding, t-distributed stochastic neighborhood embedding, and uniform manifold approximation and projection, which overcome the shortcomings of traditional visualization and dimension reduction techniques.Solutions to the book’s exercises are supplemented by R and MATLAB or SAS computer code and are available online on the Quantlet and Quantinar platforms. Practical exercises from this book and their solutions can also be found in the accompanying Springer book by W.K. Härdle and Z. Hlávka: Multivariate Statistics - Exercises and Solutions |
Beschreibung: | xv, 613 Seiten Illustrationen, Diagramme |
ISBN: | 9783031638329 |
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Datensatz im Suchindex
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Contents Part I 1 Descriptive Techniques Comparison of Batches. 1.1 Boxplots. 1.1.1 Construction of the Boxplot. 1.2 Histograms. 1.3 Kernel Densities . 1.4 Scatterplots. 1.5 Chernoff-Flury Faces. 1.6 Andrews’ Curves. 1.7 Parallel Coordinate Plots. 1.8 Hexagon Plots. 1.9 Boston Housing. 1.9.1 Aim of the Analysis. 1.9.2 What Can BeSeen from the PCPs. 1.9.3 The Scatterplot Matrix. 1.9.4 Transformations. 1.10 Exercises . References. Part II 2 Multivariate Random Variables A Short Excursion into Matrix
Algebra. 2.1 3 4 7 10 13 17 20 24 27 31 34 34 34 35 40 41 42 Elementary Operations. 2.1.1 Matrix Operations. 2.1.2 Properties of MatrixOperations. 2.1.3 Matrix Characteristics. 2.1.4 Rank. 2.1.5 Trace. 2.1.6 Determinant. 2.1.7 Transpose. 2.1.8 Inverse. 45 45 47 47 47 47 48 48 48 49 vii
Contents viii 2.1.9 G-inverse. 2.1.10 Eigenvalues, Eigenvectors. 2.1.11 Properties of Matrix Characteristics. :. Spectral Decompositions. Quadratic Forms. 2.3.1 Definiteness of Quadratic Forms and Matrices. Derivatives . Partitioned Matrices. Geometrical Aspects. 2.6.1 Distance. 2.6.2 Remark: Usefulness of Theorem 2.7. 2.6.3 Norm of a Vector. 2.6.4 Angle Between Two Vectors. 2.6.5 Rotations. . 2.6.6 Column Space and Null Space of a Matrix. 2.6.7 Projection Matrix. 2.6.8 Projection on C(X) . Exercises. 49 50 51 52 54 54 57 58 61 61 63 64 64 66 66 67 67 68 Moving to Higher Dimensions. 71 72
76 81 83 84 85 91 94 96 98 99 100 103 106 2.2 2.3 2.4 2.5 2.6 2.7 3 3.1 3.2 3.3 Covariance. Correlation. Summary Statistics . 3.3.1 Linear Transformation. 3.3.2 Mahalanobis Transformation. 3.4 Linear Model for Two Variables. 3.5 Simple Analysis of Variance. 3.5.1 The F-Test in a Linear Regression Model. 3.6 Multiple Linear Model. 3.6.1 Properties of ß. 3.6.2 The ANOVA Model in Matrix Notation. 3.7 Boston Housing . . 3.8 Exercises. References. 4 Multivariate Distributions. 4.1 4.2 4.3 Distribution and Density Function. Moments and Characteristic Functions. 4.2.1 Moments: Expectation and
Covariance Matrix. 4.2.2 Properties of the Covariance Matrix Σ = Var(X). 4.2.3 Properties of Variances and Covariances. 4.2.4 Conditional Expectations. . 4.2.5 Properties of Conditional Expectations. 4.2.6 Characteristic Functions. 4.2.7 Cumulant Functions. Transformations. 107 108 113 113 114 114 116 118 119 122 124
ix Contents 5 4.4 The Multinormal Distribution. 4.4.1 Geometry of the Νρ(μ, Σ) Distribution. 4.4.2 Singular Normal Distribution. 4.4.3 Gaussian Copula. 4.5 Sampling Distributions and Limit Theorems. 4.5.1 Transformation of Statistics . 4.6 Heavy-Tailed Distributions. 4.6.1 Generalized Hyperbolic Distribution. 4.6.2 Student’s T-Distribution. 4.6.3 Laplace Distribution. 4.6.4 Cauchy Distribution. 4.6.5 Mixture Model. 4.6.6 Multivariate Generalized Hyperbolic Distribution. 4.6.7 Multivariate T-Distribution. 4.6.8 Multivariate Laplace Distribution. 4.6.9 Multivariate Mixture Model. 4.6.10 Generalized Hyperbolic Distribution. 4.7 Copulae. 4.8 Bootstrap. 4.9 Exercises
. References. 126 128 130 130 131 136 138 139 141 142 143 146 149 152 152 153 153 155 165 168 170 Theory of the Multinormal. 171 171 176 178 180 183 185 187 Elementary' Properties of the Multinormal. 5.1.1 Conditional Approximations . 5.2 The Wishart Distribution. 5.3 Hotelling’s /^-Distribution . 5.4 Spherical and Elliptical Distributions. 5.5 Exercises . References. 5.1 6 Theory of Estimation. 6.1 The Likelihood Function. 6.2 The Cramer-Rao Lower Bound. 6.3 Exercises . Reference. 7 189 190 194 198 199 Hypothesis
Testing. 201 7.1 7.2 Likelihood Ratio Test. 7.1.1 Testing for the Mean. 7.1.2 Confidence Region for μ . Linear Hypothesis. . 7.2.1 General Framework. 7.2.2 Repeated Measurements. 7.2.3 Comparison of Two Mean Vectors. 7.2.4 Profile Analysis . 202 203 207 212 212 214 219 226
Contents X Boston Housing. 7.3.1 Testing the Equalityin Means. 7.3.2 Testing Linear Restrictions. 7.4 Exercises. References. 7.3 Part III 8 Multivariate Techniques Regression Models . 241 General ANOVA and ANCOVA Models. 8.1.1 ANOVA Models. 8.1.2 ANCOVA Models. 8.1.3 Boston Housing. . 8.2 Categorical Responses. 8.2.1 Multinomial Sampling and Contingency Tables. 8.2.2 Log-Linear Models for Contingency Tables. 8.2.3 Testing Issues with Count Data. 8.2.4 Logit Models. 8.3 Exercises. Reference. . 8.1 9 230 231 232 234 237 243 243 248 250 250 250 252 256 259 266 267 Variable
Selection. 269 Lasso. . . 9.1.1 Lasso in the Linear Regression Model. 9.1.2 Lasso in High Dimensions. 9.1.3 Lasso in Logit Model. 9.2 Elastic Net. 9.2.1 Elastic Net in the Linear Regression Model. 9.2.2 Elastic Net in the Logit Model. 9.3 Group Lasso. 9.4 Exercises. References. 270 270 280 282 285 286 288 289 292 292 10 Decomposition of Data Matrices by Factors. 295 296 297 297 298 299 299 300 300 301 301 302 304 307 9.1 10.1 10.2 10.3 10.4 10.5 10.6 The Geometric Point of View. Fitting the p-Dimensional Point Cloud. 10.2.1 Subspaces of Dimension 1. 10.2.2 Representation of the Cloud on F\. 10.2.3 Subspaces of Dimension
2. 10.2.4 Subspaces of Dimension q (q p). Fitting the «-Dimensional Point Cloud. 10.3.1 Subspaces of Dimension 1. 10.3.2 Representation of the Cloud on G1. 10.3.3 Subspaces of Dimension q (q n). Relations Between Subspaces. Practical Computation. Exercises.
xi Contents 11 Principal Component Analysis. 11.1 11.2 11.3 11.4 Standardized Linear Combination . Principal Components in Practice. Interpretation of the PCs. Asymptotic Properties of the PCs. 11.4.1 Variance Explained by the First q PCs. 11.5 Normalized Principal Component Analysis. 11.6 Principal Components as a Factorial Method. 11.6.1 Quality of the Representations. 11.7 Common Principal Components. 11.8 Boston Housing. ,. 11.9 More Examples. 11.10 Exercises. References. 12 Factor Analysis . The Orthogonal Factor Model. 12.1.1 Interpretation of the Factors. 12.1.2 Invariance of Scale. 12.1.3 Nonuniqueness of Factor
Loadings . 12.2 Estimation of the Factor Model. . 12.2.1 The Maximum Likelihood Method. 12.2.2 The Method of Principal Factors. 12.2.3 The Principal Component Method. 12.2.4 Rotation. 12.3 Factor Scores and Strategies. 12.3.1 Practical Suggestions. 12.3.2 Factor Analysis Versus PCA. 12.4 Boston Housing. 12.5 Exercises. References. 12.1 13 Cluster Analysis. 13.1 13.2 13.3 13.4 13.5 The Problem. The Proximity Between Objects. . 13.2.1 Similarity of Objects with Binary Structure. 13.2.2 Distance Measures for Continuous Variables. Cluster Algorithms. 13.3.1 Partitioning
Algorithms. 13.3.2 Hierarchical Algorithms, Agglomerative Techniques . Adaptive Weights Clustering. 13.4.1 Sequence of Radii. 13.4.2 Initialization of Weights. 13.4.3 Updates at Step к. 13.4.4 Parameter Tuning. Spectral Clustering. 309 310 314 316 320 321 323 325 327 331 334 337 343 345 347 348 351 352 352 355 357 358 360 362 363 365 365 366 368 372 373 374 375 375 377 381 381 385 392 393 393 393 396 397
xii Contents 13.5.1 Relation to the Graph Cut Problem. 13.6 Boston Housing. 13.7 Exercises. References. 14 399 401 403 406 Discriminant Analysis . 407 14.1 Allocation Rules for Known Distributions . 14.1.1 Maximum Likelihood Discriminant Rule. 14.1.2 Bayes Discriminant Rule . 14.1.3 Probability of Misclassification for the ML Rule (J = 2). 413 14.1.4 Classification with Different Covariance Matrices. , 14.2 Discrimination Rules in Practice. 14.2.1 Estimation of the Probabilities of Misclassifications . 14.2.2 Fisher’s Linear Discrimination Function. 14.3 Boston Housing. 14.4 Exercises. References. 15 Correspondence Analysis . 15.1 15.2 15.3 15.4 Motivation. Chi-Square
Decomposition. Correspondence Analysis in Practice. 15.3.1 Biplots. Exercises. 16 Canonical Correlation Analysis . 16.1 16.2 Most Interesting Linear Combination. Canonical Correlation in Practice. 16.2.1 Testing the Canonical Correlation Coefficients. 16.2.2 Canonical Correlation Analysis with Qualitative Data. 451 16.3 Exercises. . References. 17 Multidimensional Scaling . 17.1 17.2 The Problem. Metric Multidimensional Scaling. 17.2.1 The Classical Solution. 17.3 Nonmetric Multidimensional Scaling. 17.3.1 Shepard-Kruskal Algorithm. 17.4
Exercises. References. 407 408 412 414 415 416 417 421 422 423 425 426 428 432 439 441 443 443 448 450 454 454 455 455 459 460 464 465 470 471 18 Conjoint Measurement Analysis . 473 18.1 18.2 Introduction . 473 Design of Data Generation. 475
Contents 19 xiii 18.3 Estimation of Preference Orderings. 18.3.1 Metrie Solution. 18.3.2 Nonmetric Solution. 18.4 Exercises . References. 477 479 482 484 486 Applications in Finance . 487 487 488 490 492 495 497 498 499 19.1 19.2 Portfolio Choice. . Efficient Portfolio. 19.2.1 Nonexistence of a Riskless Asset. 19.2.2 Existence of a Riskless Asset. . 19.3 Efficient Portfolios in Practice. 19.4 The Capital Asset Pricing Model(CAPM). 19.5 Exercises . Reference. 20 Computationally Intensive Techniques. 501 20.1 20.2 Simplicial Depth. Projection Pursuit. 20.2.1 Exploratory Projection
Pursuit. 20.2.2 Projection Pursuit Regression. 20.3 Sliced Inverse Regression . 20.3.1 The SIR Algorithm. 20.3.2 SIR II . 20.3.3 The SIR II Algorithm. 20.4 Support Vector Machines. 20.4.1 Classification Methodology. 20.4.2 Expected vs. Empirical Risk Minimization. 20.4.3 The SVM in the Linearly Separable Case. 20.4.4 SVMs in the Linearly Nonseparable Case. 20.4.5 Nonlinear Classification . . 20.4.6 SVMs for Simulated Data. 20.4.7 Solution of the SVM Classification Problem. 20.4.8 Scoring Companies . 20.5 Classification and Regression Trees . . 20.5.1 How Does CART Work?. 20.5.2 Impurity Measures. 20.5.3 Gini Index and Twoing Rule in Practice. 20.5.4 Optimal Size of a Decision Tree. 20.5.5 Cross-Validation for Tree Pruning. 20.5.6 Cost-
Complexity Functionand Cross-Validation. 20.5.7 Regression Trees. 20.5.8 Bankruptcy Analysis. 20.6 Boston Housing. 20.7 Exercises . References. 502 505 506 508 510 512 513 514 518 519 520 523 525 528 529 530 531 534 534 535 539 540 541 542 547 548 553 554 555
xiv Contents 21 Locally Linear Embedding. 557 Introduction . The Basic Ideas of LLE. ·. The LLE Algorithm Step by Step. 21.3.1 Step 1 : k-Nearest Neighbors. 21.3.2 Step 2: Linear Approximation by the Nearest Neighbors. 561 21.3.3 Step 3: The Linear Embedding . 21.3.4 Graph-Theoretic Interpretation of the LLE Solution . 21.4 Swiss Roll Data. 21.5 Boston Housing Data. 21.6 Exercises. References. . 21.1 21.2 21.3 22 Stochastic Neighborhood Embedding. 22.1 22.2 Introduction . Modeling Neighborhood. 22.2.1 The Input Space Relies on the Gaussian Law. 22.2.2 The Embedding Space Employs the t-Distribution. 22.3 Finding the t-SNE Embedding. 22.4 Applications of
t-SNE. 22.4.1 The Trefoil Knot. 22.4.2 Quantlet Clustering . 22.5 Exercises. References. 23 Uniform Manifold Approximation and Projection. 23.1 23.2 23.3 Introduction . The Basic Ideas of UMAP. The Computational Details of UMAP. 23.3.1 The Fuzzy Topological Representation in the Input Space. 587 23.3.2 Representation in the Embedding Space. 23.3.3 Computing the Embedding. 23.4 Examples . 23.4.1 Banknotes Data. 23.4.2 The Trefoil Knot. 23.5 Exercises. References. A Symbols and
Notations. В Data. В. 1 B.2 B.3 558 559 561 561 562 564 565 566 568 568 569 570 570 570 571 573 575 575 575 580 580 581 581 582 587 589 589 592 592 593 594 595 597 601 Boston Housing Data. 601 Swiss Bank Notes. 602 Car Data. 602
Contents В .4 Classic Blue Pullovers Data. B .5 U.S. Companies Data. В .6 French Food Data. B .7 Car Marks. B .8 U.S. Crime Data. B .9 Bankruptcy Data 1. В . 10 Bankruptcy Data II. . В . 11 Journaux Data. B . 12 Timebudget Data. B . 13 Vocabulary Data. '. B . 14 French Baccalauréat Frequencies. References. Index. xv 602 603 603 603 604 604 605 605 605 607 607 607 609 |
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genre_facet | Lehrbuch |
id | DE-604.BV049865519 |
illustrated | Illustrated |
indexdate | 2024-12-02T11:02:17Z |
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isbn | 9783031638329 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035205112 |
open_access_boolean | |
owner | DE-29 DE-355 DE-BY-UBR |
owner_facet | DE-29 DE-355 DE-BY-UBR |
physical | xv, 613 Seiten Illustrationen, Diagramme |
publishDate | 2024 |
publishDateSearch | 2024 |
publishDateSort | 2024 |
publisher | Springer |
record_format | marc |
spelling | Härdle, Wolfgang 1953- Verfasser (DE-588)110357116 aut Applied multivariate statistical analysis Wolfgang Karl Härdle, Léopold Simar, Matthias R. Fengler Sixth edition Cham, Switzerland Springer [2024] xv, 613 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Now in its sixth edition, this textbook presents the tools and concepts used in multivariate data analysis in a style accessible for non-mathematicians and practitioners. Each chapter features hands-on exercises that showcase applications across various fields of multivariate data analysis. These exercises utilize high-dimensional to ultra-high-dimensional data, reflecting real-world challenges in big data analysis.For this new edition, the book has been updated and revised and now includes new chapters on modern machine learning techniques for dimension reduction and data visualization, namely locally linear embedding, t-distributed stochastic neighborhood embedding, and uniform manifold approximation and projection, which overcome the shortcomings of traditional visualization and dimension reduction techniques.Solutions to the book’s exercises are supplemented by R and MATLAB or SAS computer code and are available online on the Quantlet and Quantinar platforms. Practical exercises from this book and their solutions can also be found in the accompanying Springer book by W.K. Härdle and Z. Hlávka: Multivariate Statistics - Exercises and Solutions Statistics Social sciences—Mathematics Econometrics Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Multivariate Analyse (DE-588)4040708-1 s Statistik (DE-588)4056995-0 s Wirtschaftstheorie (DE-588)4079351-5 s 1\p DE-604 2\p DE-604 Simar, Léopold Verfasser (DE-588)123344107 aut Fengler, Matthias 1973- Verfasser (DE-588)1089931328 aut Erscheint auch als Online-Ausgabe 978-3-031-63833-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035205112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Härdle, Wolfgang 1953- Simar, Léopold Fengler, Matthias 1973- Applied multivariate statistical analysis Statistics Social sciences—Mathematics Econometrics Wirtschaftstheorie (DE-588)4079351-5 gnd Multivariate Analyse (DE-588)4040708-1 gnd Statistik (DE-588)4056995-0 gnd |
subject_GND | (DE-588)4079351-5 (DE-588)4040708-1 (DE-588)4056995-0 (DE-588)4123623-3 |
title | Applied multivariate statistical analysis |
title_auth | Applied multivariate statistical analysis |
title_exact_search | Applied multivariate statistical analysis |
title_full | Applied multivariate statistical analysis Wolfgang Karl Härdle, Léopold Simar, Matthias R. Fengler |
title_fullStr | Applied multivariate statistical analysis Wolfgang Karl Härdle, Léopold Simar, Matthias R. Fengler |
title_full_unstemmed | Applied multivariate statistical analysis Wolfgang Karl Härdle, Léopold Simar, Matthias R. Fengler |
title_short | Applied multivariate statistical analysis |
title_sort | applied multivariate statistical analysis |
topic | Statistics Social sciences—Mathematics Econometrics Wirtschaftstheorie (DE-588)4079351-5 gnd Multivariate Analyse (DE-588)4040708-1 gnd Statistik (DE-588)4056995-0 gnd |
topic_facet | Statistics Social sciences—Mathematics Econometrics Wirtschaftstheorie Multivariate Analyse Statistik Lehrbuch |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035205112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT hardlewolfgang appliedmultivariatestatisticalanalysis AT simarleopold appliedmultivariatestatisticalanalysis AT fenglermatthias appliedmultivariatestatisticalanalysis |