{"product_id":"multivariate-analysis-isbn-9781118738023","title":"Multivariate Analysis","description":"\u003cb\u003eMultivariate Analysis\u003c\/b\u003e \u003cp\u003e \u003cb\u003eComprehensive Reference Work on Multivariate Analysis and its Applications\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eThe 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. \u003c\/p\u003e\u003cp\u003eA 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:  \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eBasic properties of random vectors, copulas, normal distribution theory, and estimation \u003c\/li\u003e\n\u003cli\u003eHypothesis testing, multivariate regression, and analysis of variance \u003c\/li\u003e\n\u003cli\u003ePrincipal component analysis, factor analysis, and canonical correlation analysis \u003c\/li\u003e\n\u003cli\u003eDiscriminant analysis, cluster analysis, and multidimensional scaling \u003c\/li\u003e\n\u003cli\u003eNew advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eAlthough 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. \u003c\/p\u003e\u003cp\u003eEpigraph xvii\u003c\/p\u003e \u003cp\u003ePreface to the Second Edition xix\u003c\/p\u003e \u003cp\u003ePreface to the First Edition xxi\u003c\/p\u003e \u003cp\u003eAcknowledgments from First Edition xxv\u003c\/p\u003e \u003cp\u003eNotation, Abbreviations, and Key Ideas xxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Objects and Variables 1\u003c\/p\u003e \u003cp\u003e1.2 Some Multivariate Problems and Techniques 1\u003c\/p\u003e \u003cp\u003e1.3 The Data Matrix 7\u003c\/p\u003e \u003cp\u003e1.4 Summary Statistics 8\u003c\/p\u003e \u003cp\u003e1.5 Linear Combinations 12\u003c\/p\u003e \u003cp\u003e1.6 Geometrical Ideas 14\u003c\/p\u003e \u003cp\u003e1.7 Graphical Representation 15\u003c\/p\u003e \u003cp\u003e1.8 Measures of Multivariate Skewness and Kurtosis 20\u003c\/p\u003e \u003cp\u003eExercises and Complements 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Basic Properties of Random Vectors 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 25\u003c\/p\u003e \u003cp\u003e2.1 Cumulative Distribution Functions and Probability Density Functions 25\u003c\/p\u003e \u003cp\u003e2.2 Population Moments 27\u003c\/p\u003e \u003cp\u003e2.3 Characteristic Functions 31\u003c\/p\u003e \u003cp\u003e2.4 Transformations 32\u003c\/p\u003e \u003cp\u003e2.5 The Multivariate Normal Distribution 34\u003c\/p\u003e \u003cp\u003e2.6 Random Samples 41\u003c\/p\u003e \u003cp\u003e2.7 Limit Theorems 42\u003c\/p\u003e \u003cp\u003eExercises and Complements 44\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Nonnormal Distributions 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 49\u003c\/p\u003e \u003cp\u003e3.2 Some Multivariate Generalizations of Univariate Distributions 49\u003c\/p\u003e \u003cp\u003e3.3 Families of Distributions 52\u003c\/p\u003e \u003cp\u003e3.4 Insights into Skewness and Kurtosis 57\u003c\/p\u003e \u003cp\u003e3.5 Copulas 60\u003c\/p\u003e \u003cp\u003eExercises and Complements 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Normal Distribution Theory 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction and Characterization 71\u003c\/p\u003e \u003cp\u003e4.2 Linear Forms 73\u003c\/p\u003e \u003cp\u003e4.3 Transformations of Normal Data Matrices 75\u003c\/p\u003e \u003cp\u003e4.4 The Wishart Distribution 77\u003c\/p\u003e \u003cp\u003e4.5 The Hotelling T\u003csup\u003e2\u003c\/sup\u003e Distribution 83\u003c\/p\u003e \u003cp\u003e4.6 Mahalanobis Distance 85\u003c\/p\u003e \u003cp\u003e4.7 Statistics Based on the Wishart Distribution 88\u003c\/p\u003e \u003cp\u003e4.8 Other Distributions Related to the Multivariate Normal 92\u003c\/p\u003e \u003cp\u003eExercises and Complements 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Estimation 101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 101\u003c\/p\u003e \u003cp\u003e5.1 Likelihood and Sufficiency 101\u003c\/p\u003e \u003cp\u003e5.2 Maximum-likelihood Estimation 106\u003c\/p\u003e \u003cp\u003e5.3 Robust Estimation of Location and Dispersion for Multivariate Distributions 112\u003c\/p\u003e \u003cp\u003e5.4 Bayesian Inference 117\u003c\/p\u003e \u003cp\u003eExercises and Complements 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Hypothesis Testing 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 125\u003c\/p\u003e \u003cp\u003e6.2 The Techniques Introduced 127\u003c\/p\u003e \u003cp\u003e6.3 The Techniques Further Illustrated 134\u003c\/p\u003e \u003cp\u003e6.4 Simultaneous Confidence Intervals 142\u003c\/p\u003e \u003cp\u003e6.5 The Behrens–Fisher Problem 144\u003c\/p\u003e \u003cp\u003e6.6 Multivariate Hypothesis Testing: Some General Points 145\u003c\/p\u003e \u003cp\u003e6.7 Nonnormal Data 146\u003c\/p\u003e \u003cp\u003e6.8 Mardia’s Nonparametric Test for the Bivariate Two-sample Problem 149\u003c\/p\u003e \u003cp\u003eExercises and Complements 151\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Multivariate Regression Analysis 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 159\u003c\/p\u003e \u003cp\u003e7.2 Maximum-likelihood Estimation 160\u003c\/p\u003e \u003cp\u003e7.3 The General Linear Hypothesis 162\u003c\/p\u003e \u003cp\u003e7.4 Design Matrices of Degenerate Rank 165\u003c\/p\u003e \u003cp\u003e7.5 Multiple Correlation 167\u003c\/p\u003e \u003cp\u003e7.6 Least-squares Estimation 171\u003c\/p\u003e \u003cp\u003e7.7 Discarding of Variables 174\u003c\/p\u003e \u003cp\u003eExercises and Complements 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Graphical Models 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 183\u003c\/p\u003e \u003cp\u003e8.2 Graphs and Conditional Independence 184\u003c\/p\u003e \u003cp\u003e8.3 Gaussian Graphical Models 188\u003c\/p\u003e \u003cp\u003e8.4 Log-linear Graphical Models 195\u003c\/p\u003e \u003cp\u003e8.5 Directed and Mixed Graphs 202\u003c\/p\u003e \u003cp\u003eExercises and Complements 204\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Principal Component Analysis 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 207\u003c\/p\u003e \u003cp\u003e9.2 Definition and Properties of Principal Components 207\u003c\/p\u003e \u003cp\u003e9.3 Sampling Properties of Principal Components 221\u003c\/p\u003e \u003cp\u003e9.4 Testing Hypotheses About Principal Components 227\u003c\/p\u003e \u003cp\u003e9.5 Correspondence Analysis 230\u003c\/p\u003e \u003cp\u003e9.6 Allometry – Measurement of Size and Shape 237\u003c\/p\u003e \u003cp\u003e9.7 Discarding of Variables 240\u003c\/p\u003e \u003cp\u003e9.8 Principal Component Regression 241\u003c\/p\u003e \u003cp\u003e9.9 Projection Pursuit and Independent Component Analysis 244\u003c\/p\u003e \u003cp\u003e9.10 PCA in High Dimensions 247\u003c\/p\u003e \u003cp\u003eExercises and Complements 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Factor Analysis 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 259\u003c\/p\u003e \u003cp\u003e10.2 The Factor Model 260\u003c\/p\u003e \u003cp\u003e10.3 Principal Factor Analysis 264\u003c\/p\u003e \u003cp\u003e10.4 Maximum-likelihood Factor Analysis 266\u003c\/p\u003e \u003cp\u003e10.5 Goodness-of-fit Test 269\u003c\/p\u003e \u003cp\u003e10.6 Rotation of Factors 270\u003c\/p\u003e \u003cp\u003e10.7 Factor Scores 275\u003c\/p\u003e \u003cp\u003e10.8 Relationships Between Factor Analysis and Principal Component Analysis 276\u003c\/p\u003e \u003cp\u003e10.9 Analysis of Covariance Structures 277\u003c\/p\u003e \u003cp\u003eExercises and Complements 277\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Canonical Correlation Analysis 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 281\u003c\/p\u003e \u003cp\u003e11.2 Mathematical Development 282\u003c\/p\u003e \u003cp\u003e11.3 Qualitative Data and Dummy Variables 288\u003c\/p\u003e \u003cp\u003e11.4 Qualitative and Quantitative Data 290\u003c\/p\u003e \u003cp\u003eExercises and Complements 293\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Discriminant Analysis and Statistical Learning 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 297\u003c\/p\u003e \u003cp\u003e12.2 Bayes’ Discriminant Rule 299\u003c\/p\u003e \u003cp\u003e12.3 The Error Rate 300\u003c\/p\u003e \u003cp\u003e12.4 Discrimination Using the Normal Distribution 304\u003c\/p\u003e \u003cp\u003e12.5 Discarding of Variables 312\u003c\/p\u003e \u003cp\u003e12.6 Fisher’s Linear Discriminant Function 314\u003c\/p\u003e \u003cp\u003e12.7 Nonparametric Distance-based Methods 319\u003c\/p\u003e \u003cp\u003e12.8 Classification Trees 323\u003c\/p\u003e \u003cp\u003e12.9 Logistic Discrimination 332\u003c\/p\u003e \u003cp\u003e12.10 Neural Networks 336\u003c\/p\u003e \u003cp\u003eExercises and Complements 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Multivariate Analysis of Variance 355\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 355\u003c\/p\u003e \u003cp\u003e13.2 Formulation of Multivariate One-way Classification 355\u003c\/p\u003e \u003cp\u003e13.3 The Likelihood Ratio Principle 356\u003c\/p\u003e \u003cp\u003e13.4 Testing Fixed Contrasts 358\u003c\/p\u003e \u003cp\u003e13.5 Canonical Variables and A Test of Dimensionality 359\u003c\/p\u003e \u003cp\u003e13.6 The Union Intersection Approach 369\u003c\/p\u003e \u003cp\u003e13.7 Two-way Classification 370\u003c\/p\u003e \u003cp\u003eExercises and Complements 375\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Cluster Analysis and Unsupervised Learning 379\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 379\u003c\/p\u003e \u003cp\u003e14.2 Probabilistic Membership Models 380\u003c\/p\u003e \u003cp\u003e14.3 Parametric Mixture Models 384\u003c\/p\u003e \u003cp\u003e14.4 Partitioning Methods 386\u003c\/p\u003e \u003cp\u003e14.5 Hierarchical Methods 391\u003c\/p\u003e \u003cp\u003e14.6 Distances and Similarities 397\u003c\/p\u003e \u003cp\u003e14.7 Grouped Data 404\u003c\/p\u003e \u003cp\u003e14.8 Mode Seeking 406\u003c\/p\u003e \u003cp\u003e14.9 Measures of Agreement 408\u003c\/p\u003e \u003cp\u003eExercises and Complements 412\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Multidimensional Scaling 419\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 419\u003c\/p\u003e \u003cp\u003e15.2 Classical Solution 421\u003c\/p\u003e \u003cp\u003e15.3 Duality Between Principal Coordinate Analysis and Principal Component Analysis 428\u003c\/p\u003e \u003cp\u003e15.4 Optimal Properties of the Classical Solution and Goodness of Fit 429\u003c\/p\u003e \u003cp\u003e15.5 Seriation 436\u003c\/p\u003e \u003cp\u003e15.6 Nonmetric Methods 438\u003c\/p\u003e \u003cp\u003e15.7 Goodness of Fit Measure: Procrustes Rotation 440\u003c\/p\u003e \u003cp\u003e15.8 Multisample Problem and Canonical Variates 443\u003c\/p\u003e \u003cp\u003eExercises and Complements 444\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 High-dimensional Data 449\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 449\u003c\/p\u003e \u003cp\u003e16.2 Shrinkage Methods in Regression 451\u003c\/p\u003e \u003cp\u003e16.3 Principal Component Regression 455\u003c\/p\u003e \u003cp\u003e16.4 Partial Least Squares Regression 457\u003c\/p\u003e \u003cp\u003e16.5 Functional Data 465\u003c\/p\u003e \u003cp\u003eExercises and Complements 473\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Matrix Algebra 475\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Introduction 475\u003c\/p\u003e \u003cp\u003eA.2 Matrix Operations 478\u003c\/p\u003e \u003cp\u003eA.3 Further Particular Matrices and Types of Matrices 483\u003c\/p\u003e \u003cp\u003eA.4 Vector Spaces, Rank, and Linear Equations 485\u003c\/p\u003e \u003cp\u003eA.5 Linear Transformations 488\u003c\/p\u003e \u003cp\u003eA.6 Eigenvalues and Eigenvectors 488\u003c\/p\u003e \u003cp\u003eA.7 Quadratic Forms and Definiteness 495\u003c\/p\u003e \u003cp\u003eA.8 Generalized Inverse 497\u003c\/p\u003e \u003cp\u003eA.9 Matrix Differentiation and Maximization Problems 499\u003c\/p\u003e \u003cp\u003eA.10 Geometrical Ideas 501\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Univariate Statistics 505\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Introduction 505\u003c\/p\u003e \u003cp\u003eB.2 Normal Distribution 505\u003c\/p\u003e \u003cp\u003eB.3 Chi-squared Distribution 506\u003c\/p\u003e \u003cp\u003eB.4 F and Beta Variables 506\u003c\/p\u003e \u003cp\u003eB.5 t Distribution 507\u003c\/p\u003e \u003cp\u003eB.6 Poisson Distribution 507\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC R commands and Data 509\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Basic R Commands Related to Matrices 509\u003c\/p\u003e \u003cp\u003eC.2 R Libraries and Commands Used in Exercises and Figures 510\u003c\/p\u003e \u003cp\u003eC.3 Data Availability 511\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD Tables 513\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences and Author Index 523\u003c\/p\u003e \u003cp\u003eIndex 543\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eKanti V. Mardia OBE \u003c\/b\u003e 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.  \u003c\/p\u003e\u003cp\u003e\u003cb\u003eJohn T. Kent \u003c\/b\u003e and \u003cb\u003eCharles C. Taylor \u003c\/b\u003e are both Professors in the Department of Statistics, University of Leeds.   \u003c\/p\u003e\u003cp\u003e \u003cb\u003eComprehensive Reference Work on Multivariate Analysis and its Applications\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eThe 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. \u003c\/p\u003e\u003cp\u003eA 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:  \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eBasic properties of random vectors, copulas, normal distribution theory, and estimation \u003c\/li\u003e\n\u003cli\u003eHypothesis testing, multivariate regression, and analysis of variance \u003c\/li\u003e\n\u003cli\u003ePrincipal component analysis, factor analysis, and canonical correlation analysis \u003c\/li\u003e\n\u003cli\u003eDiscriminant analysis, cluster analysis, and multidimensional scaling \u003c\/li\u003e\n\u003cli\u003eNew advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eAlthough 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989664153829,"sku":"NP9781118738023","price":81.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118738023.jpg?v=1761785013","url":"https:\/\/k12savings.com\/es\/products\/multivariate-analysis-isbn-9781118738023","provider":"K12savings","version":"1.0","type":"link"}