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The Geometry of Multivariate Statistics

2014-02-25 Psychology
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Release : 2014-02-25
Genre : Psychology
Kind : eBook
Book Rating : 221/5 ( reviews)

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Book Synopsis The Geometry of Multivariate Statistics by : Thomas D. Wickens

Download or read book The Geometry of Multivariate Statistics written by Thomas D. Wickens. This book was released on 2014-02-25. Available in PDF, EPUB and Kindle. Book excerpt: A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables. This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.

Mathematical Tools for Applied Multivariate Analysis

2014-05-10 Mathematics
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Release : 2014-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 044/5 ( reviews)

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Book Synopsis Mathematical Tools for Applied Multivariate Analysis by : Paul E. Green

Download or read book Mathematical Tools for Applied Multivariate Analysis written by Paul E. Green. This book was released on 2014-05-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multivariate Statistics

2007 Mathematics
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Release : 2007
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Multivariate Statistics by : Morris L. Eaton

Download or read book Multivariate Statistics written by Morris L. Eaton. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: Building from his lecture notes, Eaton (mathematics, U. of Minnesota) has designed this text to support either a one-year class in graduate-level multivariate courses or independent study. He presents a version of multivariate statistical theory in which vector space and invariance methods replace to a large extent more traditional multivariate methods. Using extensive examples and exercises Eaton describes vector space theory, random vectors, the normal distribution on a vector space, linear statistical models, matrix factorization and Jacobians, topological groups and invariant measures, first applications of invariance, the Wishart distribution, inferences for means in multivariate linear models and canonical correlation coefficients. Eaton also provides comments on selected exercises and a bibliography.

Theory of Multivariate Statistics

2008-01-20 Mathematics
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Release : 2008-01-20
Genre : Mathematics
Kind : eBook
Book Rating : 168/5 ( reviews)

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Book Synopsis Theory of Multivariate Statistics by : Martin Bilodeau

Download or read book Theory of Multivariate Statistics written by Martin Bilodeau. This book was released on 2008-01-20. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a textbook for students taking a first graduate course in the subject, as well as for the general reference of interested research workers, this text discusses, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, such as robust inference and the use of the bootstrap in a multivariate setting. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear algebra.

Aspects of Multivariate Statistical Theory

2009-09-25 Mathematics
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Release : 2009-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 705/5 ( reviews)

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Book Synopsis Aspects of Multivariate Statistical Theory by : Robb J. Muirhead

Download or read book Aspects of Multivariate Statistical Theory written by Robb J. Muirhead. This book was released on 2009-09-25. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to penetrate deeper into the multivariate field." -Mededelingen van het Wiskundig Genootschap "This book is a comprehensive and clearly written text on multivariate analysis from a theoretical point of view." -The Statistician Aspects of Multivariate Statistical Theory presents a classical mathematical treatment of the techniques, distributions, and inferences based on multivariate normal distribution. Noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis are introduced. Advances in multivariate analysis are discussed, including decision theory and robustness. The book also includes tables of percentage points of many of the standard likelihood statistics used in multivariate statistical procedures. This definitive resource provides in-depth discussion of the multivariate field and serves admirably as both a textbook and reference.

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