Synopses & Reviews
This is author-approved bcc: Multivariate statistical methods have evolved from the pioneering work of Fisher, Pearson, Hotelling,and others, motivated by practical problems in biological and other sciences. In the past fifty years the field has grown rapidly, largely due to the availability of computers that make the calculations feasible. This book gives a comprehensive and self-contained introduction, carefully balancing mathematical theory and practical applications. "A First Course in Multivariate Statistics" starts at an elementary level, developing concepts of multivariate distributions from first principles. A chapter on the multivariate normal distribution reviews the classical parametric theory. Methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, are at the core of the book. Methods of testing hypotheses are developed from heuristic principles, followed by likelihood ratio tests and permutation tests. The powerful self- consistency principle is used to introduce principal components as a method of approximation. The book concludes with a chapter on finite mixture analysis, a topic of great practical and theoretical importance. Unique features of "A First Course in Multivariate Statistics" include the presentation of the EM algorithm for maximum likelihood estimation with incomplete data, resampling based methods of testing, a brief introduction to the theory of elliptical distributions, and a comparison of linear and quadratic classification rules. Examples from biology, anthropology, chemistry, and other area are worked out
Review
From a review: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION "... is actually a very unique book that differs considerably from other multivariate texts. Flury should be applauded for his intention and effort to produce a new type of multivariate book that is neither a comprehensive theoretical treatise nor an encyclopedic methods cookbook. ... it is a welcome addition to the multivariate statistics literature. This is a well-written book with vivid and lively discussions."
Review
From a review:
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
"... is actually a very unique book that differs considerably from other multivariate texts. Flury should be applauded for his intention and effort to produce a new type of multivariate book that is neither a comprehensive theoretical treatise nor an encyclopedic methods cookbook. ... it is a welcome addition to the multivariate statistics literature. This is a well-written book with vivid and lively discussions."
Synopsis
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."
Synopsis
A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate distributions from first principles. After a chapter on the multivariate normal distribution reviewing the classical parametric theory, methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests. Finally, the powerful self-consistency principle is used to introduce principal components as a method of approximation, rounded off by a chapter on finite mixture analysis.
Description
Includes bibliographical references (. [703]-709) and index.
Table of Contents
Why Multivariate Statistics?- Joint Distribution of Several Random Variables.- The Multivariate Normal Distribution.- Parameter Estimation.- Discrimination and Classification, Round 1.- Statistical Inference for Means.- Discrimination and Classification, Round 2.- Linear Principal Component Analysis.- Normal Mixtures.