Mathematical Tools For Applied Multivariate Analysis

Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the mathematical foundations of applied multivariate analysis. Organized into six chapters, this book begins with an overview of the three problems in multiple regression, principal components analysis, and multiple discriminant analysis. This text then presents a standard treatment of the mechanics of matrix algebra, including definitions and operations on matrices, vectors, and determinants. Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. This book discusses as well the eigenstructures and quadratic forms. The final chapter deals with the geometric aspects of linear transformations. This book is a valuable resource for students.

The nature of multivariate data analysis; Vector and matrix operations for multivariate analysis; Vector and matrix concepts from a geometric viewpoint; Linear transformations from a geometric viewpoint; Decomposition of matrix transformations: eigenstructures and quadratic forms; Applying the tools to multivariate data.

Multivariate statistics and mathematical models provide flexible and powerful tools essential in most disciplines. Nevertheless, many practicing researchers lack an adequate knowledge of these techniques, or did once know the techniques, but have not been able to keep abreast of new developments. The Handbook of Applied Multivariate Statistics and Mathematical Modeling explains the appropriate uses of multivariate procedures and mathematical modeling techniques, and prescribe practices that enable applied researchers to use these procedures effectively without needing to concern themselves with the mathematical basis. The Handbook emphasizes using models and statistics as tools. The objective of the book is to inform readers about which tool to use to accomplish which task. Each chapter begins with a discussion of what kinds of questions a particular technique can and cannot answer. As multivariate statistics and modeling techniques are useful across disciplines, these examples include issues of concern in biological and social sciences as well as the humanities.

Green's name appears first on the earlier edition.

Focusing on high-dimensional applications, this 4th edition presents the tools and concepts used in multivariate data analysis in a style that is also accessible for non-mathematicians and practitioners. All chapters include practical exercises that highlight applications in different multivariate data analysis fields. All of the examples involve high to ultra-high dimensions and represent a number of major fields in big data analysis. The fourth edition of this book on Applied Multivariate Statistical Analysis offers the following new features: A new chapter on Variable Selection (Lasso, SCAD and Elastic Net) All exercises are supplemented by R and MATLAB code that can be found on www.quantlet.de. The practical exercises include solutions that can be found in Härdle, W. and Hlavka, Z., Multivariate Statistics: Exercises and Solutions. Springer Verlag, Heidelberg.

Like most academic authors, my views are a joint product of my teaching and my research. Needless to say, my views reflect the biases that I have acquired. One way to articulate the rationale (and limitations) of my biases is through the preface of a truly great text of a previous era, Cooley and Lohnes (1971, p. v). They draw a distinction between mathematical statisticians whose intel lect gave birth to the field of multivariate analysis, such as Hotelling, Bartlett, and Wilks, and those who chose to "concentrate much of their attention on methods of analyzing data in the sciences and of interpreting the results of statistical analysis . . . . (and) . . . who are more interested in the sciences than in mathematics, among other characteristics. " I find the distinction between individuals who are temperamentally "mathe maticians" (whom philosophy students might call "Platonists") and "scientists" ("Aristotelians") useful as long as it is not pushed to the point where one assumes "mathematicians" completely disdain data and "scientists" are never interested in contributing to the mathematical foundations of their discipline. I certainly feel more comfortable attempting to contribute in the "scientist" rather than the "mathematician" role. As a consequence, this book is primarily written for individuals concerned with data analysis. However, as noted in Chapter 1, true expertise demands familiarity with both traditions.

This book provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear multivariate models and exploratory data analysis techniques. Each chapter contains the development of basic theoretical results with numerous applications illustrated using examples from the social and behavioral sciences, and other disciplines. All examples are analyzed using SAS for Windows Version 8.0.

The authors have cleverly used exercises and their solutions to explore the concepts of multivariate data analysis. Broken down into three sections, this book has been structured to allow students in economics and finance to work their way through a well formulated exploration of this core topic. The first part of this book is devoted to graphical techniques. The second deals with multivariate random variables and presents the derivation of estimators and tests for various practical situations. The final section contains a wide variety of exercises in applied multivariate data analysis.