A First Course in Multivariate Statistics

Springer Science & Business Media, Aug 15, 1997 - Mathematics - 713 pages
My goal in writing this book has been to provide teachers and students of multi variate statistics with a unified treatment ofboth theoretical and practical aspects of this fascinating area. The text is designed for a broad readership, including advanced undergraduate students and graduate students in statistics, graduate students in bi ology, anthropology, life sciences, and other areas, and postgraduate students. The style of this book reflects my beliefthat the common distinction between multivariate statistical theory and multivariate methods is artificial and should be abandoned. I hope that readers who are mostly interested in practical applications will find the theory accessible and interesting. Similarly I hope to show to more mathematically interested students that multivariate statistical modelling is much more than applying formulas to data sets. The text covers mostly parametric models, but gives brief introductions to computer-intensive methods such as the bootstrap and randomization tests as well. The selection of material reflects my own preferences and views. My principle in writing this text has been to restrict the presentation to relatively few topics, but cover these in detail. This should allow the student to study an area deeply enough to feel comfortable with it, and to start reading more advanced books or articles on the same topic.

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Really comprehensive and well presented. shows the beauty of statistics.

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great book. Straight to the point and Very helpful!

Contents

 Why Multivariate Statistics? 1 Exercises for Chapter 1 18 Joint Distribution of Several Random Variables 23 22 Probability Density Function and Distribution Function of a Bivariate Random Variable 25 23 Marginal Distributions 38 24 Independence of Random Variables 47 25 Expected Values Moments Covariance and Correlation 57 26 Conditional Distributions 75
 66 UnionIntersection and Likelihood Ratio Testing 418 67 ResamplingBased Testing 435 Discrimination and Classification Round 2 453 Linear vs Quadratic 460 73 Canonical Discriminant Functions 485 74 Multivariate Analysis of Variance 509 75 Simple Logistic Regression 519 76 Multiple Logistic Regression 538

 27 Conditional Expectation and Regression 89 28 Mixed DiscreteContinuous Distributions and Finite Mixtures 104 29 Sums of Random Variables 130 210 Notions and Concepts of pvariate Distributions 140 211 Transformations of Random Vectors 155 The Multivariate Normal Distribution 171 32 Definition and Properties of the Multivariate Normal Distribution 175 33 Further Properties of the Multivariate Normal Distribution 186 34 Spherical and Elliptical Distributions 197 Parameter Estimation 209 42 Plugin Estimators 216 43 Maximum Likelihood Estimation 233 44 Maximum Likelihood Estimation with Incomplete Data 260 Discrimination and Classification Round 1 279 52 Standard Distance and the Linear Discriminant Function 280 53 Using the Linear Discriminant Function 302 54 Normal Theory Linear Discrimination 323 55 Error Rates 344 56 Linear Discriminant Functions and Conditional Means 357 Statistical Inference for Means 375 62 The OneSample PTest 377 63 Confidence Regions for Mean Vectors 391 64 The TwoSample Ptest 402 65 Inference for Discriminant Function Coefficients 408
 Linear Principal Component Analysis 563 82 SelfConsistent Approximations 568 83 SelfConsistent Projections and Orthogonal Least Squares 578 84 Properties of Linear Principal Components 592 85 Applications 605 86 Sampling Properties 617 87 Outlook 625 Normal Mixtures 639 92 Maximum Likelihood Estimation 645 93 The EMAlgorithm for Normal Mixtures 656 94 Examples 663 Normal Theory Discrimination with Partially Classified Data 679 Selected Results From Matrix Algebra 687 A1 Partitioned Matrices 688 A2 Positive Definite Matrices 689 A3 The Cholesky Decomposition 690 A4 Vector and Matrix Differentiation 691 A5 Eigenvectors and Eigenvalues 692 A6 Spectral Decomposition of Symmetric Matrices 693 A7 The Square Root of a Positive Definite Symmetric Matrix 695 Bibliography 703 Index 711 Copyright