Multivariate Analysis

Kanti V. Mardia , John T. Kent , Charles C. Taylor 지음

Wiley 2024년 07월 03일 출간

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Multivariate Analysis Comprehensive Reference Work on Multivariate Analysis and its Applications The first edition of this book, by Mardia, Kent and Bibby, has been used globally for over 40 years. This second edition brings many topics up to date, with a special emphasis on recent developments. A wide range of material in multivariate analysis is covered, including the classical themes of multivariate normal theory, multivariate regression, inference, multidimensional scaling, factor analysis, cluster analysis and principal component analysis. The book also now covers modern developments such as graphical models, robust estimation, statistical learning, and high-dimensional methods. The book expertly blends theory and application, providing numerous worked examples and exercises at the end of each chapter. The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are appendices which provide a background in matrix algebra, a summary of univariate statistics, a collection of statistical tables and a discussion of computational aspects. The work includes coverage of: Basic properties of random vectors, copulas, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Discriminant analysis, cluster analysis, and multidimensional scaling New advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data Although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, the book will also be of interest to research workers and applied scientists.

목차

Epigraph Preface xiii Preface to the Second Edition xiii Preface to the First Edition xv Acknowledgements from First Edition xviii Notation, abbreviations and key ideas xix 1 Introduction 1 1.1 Objects and Variables 1 1.2 Some Multivariate Problems and Techniques 2 1.2.1 Generalizations of univariate techniques 2 1.2.2 Dependence and regression 2 1.2.3 Linear combinations 2 1.2.4 Assignment and dissection 5 1.2.5 Building configurations 6 1.3 The Data Matrix 6 1.4 Summary Statistics 7 1.4.1 The mean vector and covariance matrix 8 1.4.2 Measures of multivariate scatter 11 1.5 Linear Combinations 11 1.5.1 The scaling transformation 12 1.5.2 Mahalanobis transformation 12 1.5.3 Principal component transformation 12 1.6 Geometrical Ideas 13 1.7 Graphical Representation 14 1.7.1 Univariate scatters 14 1.7.2 Bivariate scatters 16 1.7.3 Harmonic curves 16 1.7.4 Parallel coordinates plot 19 1.8 Measures of Multivariate Skewness and Kurtosis 19 2 Basic Properties of Random Vectors 27 2.1 Cumulative Distribution Functions and Probability Density Functions 27 2.2 Population Moments 29 2.2.1 Expectation and correlation 29 2.2.2 Population mean vector and covariance matrix 29 2.2.3 Mahalanobis space 31 2.2.4 Higher moments 31 2.2.5 Conditional moments 33 2.3 Characteristic Functions 33 2.4 Transformations 35 2.5 The Multivariate Normal Distribution 36 2.5.1 Definition 36 2.5.2 Geometry 38 2.5.3 Properties 38 2.5.4 Singular multivariate normal distribution 43 2.5.5 The matrix normal distribution 44 2.6 Random Samples 45 2.7 Limit Theorems 47 3 Non-normal Distributions 53 3.1 Introduction 53 3.2 Some Multivariate Generalizations of U

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저자(글) Kanti V. Mardia

저자(글) John T. Kent

저자(글) Charles C. Taylor