Informationen zum Autor Kanti V. Mardia is a Senior Research Professor in the Department of Statistics at the University of Leeds, Leverhulme Emeritus Fellow, and Visiting Professor in the Department of Statistics, University of Oxford.John T. Kent and Charles C. Taylor are both Professors in the Department of Statistics, University of Leeds. Klappentext Comprehensive Reference Work on Multivariate Analysis and Its ApplicationsThe first edition of this book, by Mardia, Kent and Bibby, has been widely 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, factoranalysis, 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, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Cluster analysis and multidimensional scaling New advances and techniques, including statistical learning, graphical models and regularization methods for high-dimensional dataAlthough 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. Zusammenfassung Comprehensive Reference Work on Multivariate Analysis and Its ApplicationsThe first edition of this book, by Mardia, Kent and Bibby, has been widely 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, factoranalysis, 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, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Cluster analysis and multidimensional scaling New advances and techniques, including statistical learning, graphical models and regularization methods for high-dimensional dataAlthough 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 ...

Autorentext
Kanti V. Mardia is a Senior Research Professor in the Department of Statistics at the University of Leeds, Leverhulme Emeritus Fellow, and Visiting Professor in the Department of Statistics, University of Oxford. John T. Kent and Charles C. Taylor are both Professors in the Department of Statistics, University of Leeds.

Klappentext

Comprehensive Reference Work on Multivariate Analysis and Its Applications The first edition of this book, by Mardia, Kent and Bibby, has been widely 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, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Cluster analysis and multidimensional scaling * New advances and techniques, including 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.

Inhalt
1 response variables 493 16.4.4 The predictor envelope model 494 16.4.5 PLS regression 494 16.4.6 Joint envelope models 496 16.5 Functional Data 498 16.5.1 Functional principal component analysis 499 16.5.2 Functional linear regression models 503 A Matrix Algebra 509 A.1 Introduction 509 A.2 Matrix Operations 512 A.2.1 Transpose 512 A.2.2 Trace 513 A.2.3 Determinants and cofactors 513 A.2.4 Inverse 515 A.2.5 Kronecker products 516 A.3 Further Particular Matrices and Types of Matrix 517 A.3.1 Orthogonal matrices 517 A.3.2 Equicorrelation matrix 518 A.3.3 Centering matrix 519 A.4 Vector Spaces, Rank, and Linear Equations 519 A.4.1 Vector spaces 519 A.4.2 Rank 521 A.4.3 Linear equations 522 A.5 Linear Transformations 523 A.6 Eigenvalues and Eigenvectors 523 A.6.1 General results 523 A.6.2 Symmetric matrices 525 A.7 Quadratic Forms and Definiteness 531 A.8 Generalized Inverse 533 A.9 Matrix Differentiation and Maximization Problems 535 A.10 Geometrical Ideas 538 A.10.1 n-dimensional geometry 538 A.10.2 Orthogonal transformations 538 A.10.3 Projections 539 A.10.4 Ellipsoids 539 B Univariate Statistics 543 B.1 Introduction 543 B.2 Normal Distribution 543 B.3 Chi-squared Distribution 544 B.4 F and Beta Variables 544 B.5 t distribution 545 B.6 Poisson distribution 546 C R commands and data 547 C.1 Basic R Commands Related to Matrices 547 C.2 R Libraries and Commands Used in Exercises and Figures 548 C.3 Data Availability 549 D Tables 551 References 560 Index