Multivariate Analysis 3e

3rd Auflage
ISBN: 978-0-470-17896-6
Verlag: Wiley

Buch, Englisch, 800 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1346 g

Reihe: Wiley Series in Probability and Statistics

Praise for the Second Edition

"This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight. There is much practical wisdom in this book that is hard to find elsewhere."
-IIE Transactions

Filled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a "methods" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations.

This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including t-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including:

* Confirmatory Factor Analysis
* Classification Trees
* Dynamic Graphics
* Transformations to Normality
* Prediction for Multivariate Multiple Regression
* Kronecker Products and Vec Notation

New exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS(r) code.

Requiring only a basic background in statistics, Methods of Multivariate Analysis, Third Edition is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.

Autoren/Hrsg.

Rencher, Alvin C

Christensen, William F

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Preface xvii

Acknowledgments xxi

1 Introduction 1

1.1 Why Multivariate Analysis? 1

1.2 Prerequisites 3

1.3 Objectives 3

1.4 Basic Types of Data And Analysis 4

2 Matrix Algebra 7

2.1 Introduction 7

2.2 Notation and Basic Definitions 8

2.3 Operations 11

2.4 Partitioned Matrices 22

2.5 Rank 23

2.6 Inverse 25

2.7 Positive Definite Matrices 26

2.8 Determinants 28

2.9 Trace 31

2.10 Orthogonal Vectors and Matrices 31

2.11 Eigenvalues and Eigenvectors 32

2.12 Kronecker and VEC Notation 37

Problems 39

3 Characterizing and Displaying Multivariate Data 47

3.1 Mean and Variance of a Univariate Random Variable 47

3.2 Covariance and Correlation Of Bivariate Random Variables 49

3.3 Scatter Plots of Bivariate Samples 55

3.4 Graphical Displays for Multivariate Samples 56

3.5 Dynamic Graphics 58

3.6 Mean Vectors 63

3.7 Covariance Matrices 66

3.8 Correlation Matrices 69

3.9 Mean Vectors and Covariance Matrices for Subsets of Variables 71

3.9.1 Two Subsets 71

3.9.2 Three or More Subsets 73

3.10 Linear Combinations of Variables 75

3.10.1 Sample Properties 75

3.10.2 Population Properties 81

3.11 Measures of Overall Variability 81

3.12 Estimation of Missing Values 82

3.13 Distance Between Vectors 84

Problems 85

4 The Multivariate Normal Distribution 91

4.1 Multivariate Normal Density Function 91

4.2 Properties of Multivariate Normal Random Variables 94

4.3 Estimation in the Multivariate Normal 99

4.4 Assessing Multivariate Normality 101

4.5 Transformations to Normality 108

4.6 Outliers 111

Problems 117

5 Tests on One or Two Mean Vectors 125

5.1 Multivariate Versus Univariate Tests 125

5.2 Tests on µ With ??Known 126

5.3 Tests on µ When ??is Unknown 130

Über Autor(innen)

ALVIN C. RENCHER is Professor Emeritus in the Department of Statistics at Brigham Young University. A Fellow of the American Statistical Association, he is the author of Linear Models in Statistics, Second Edition and Multivariate Statistical Inference and Applications, both published by Wiley.

WILLIAM F. CHRISTENSEN is Professor in the Department of Statistics at Brigham Young University. He has been published extensively in his areas of research interest, which include multivariate analysis, resampling methods, and spatial and environmental statistics.