The Geometry Of Multivariate Statistics

Author : Thomas D. Wickens
Publisher : Psychology Press
Page : 216 pages
File Size : 48,9 Mb
Release : 2014-02-25
Category : Psychology
ISBN : 9781317780229

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The Geometry of Multivariate Statistics by Thomas D. Wickens Pdf

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.

Author : Regina Y. Liu,Robert Joseph Serfling,Diane L. Souvaine
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 48,5 Mb
Release : 2006
Category : Geometry
ISBN : 9780821835968

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Data Depth by Regina Y. Liu,Robert Joseph Serfling,Diane L. Souvaine Pdf

The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many of the articles in the book lay down the foundations for further collaboration and interdisciplinary research. Information for our distributors: Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).

Author : Ian L. Dryden,John T. Kent
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 55,5 Mb
Release : 2015-09-03
Category : Mathematics
ISBN : 9781118866603

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Geometry Driven Statistics by Ian L. Dryden,John T. Kent Pdf

A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia’s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field. Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.

Author : Morris L. Eaton
Publisher : Unknown
Page : 528 pages
File Size : 55,5 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015069032285

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Multivariate Statistics by Morris L. Eaton Pdf

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.

Author : Martin Bilodeau,David Brenner
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 48,6 Mb
Release : 1999-08-05
Category : Mathematics
ISBN : 9780387987392

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Theory of Multivariate Statistics by Martin Bilodeau,David Brenner Pdf

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.

Author : Paul E. Green
Publisher : Academic Press
Page : 402 pages
File Size : 54,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483214047

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Mathematical Tools for Applied Multivariate Analysis by Paul E. Green Pdf

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.

Author : Richard A. Johnson,Dean W. Wichern
Publisher : Unknown
Page : 767 pages
File Size : 49,6 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:769986191

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Applied Multivariate Statistical Analysis by Richard A. Johnson,Dean W. Wichern Pdf

Author : Brigitte Le Roux,Henry Rouanet
Publisher : Springer Science & Business Media
Page : 475 pages
File Size : 49,8 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9781402022364

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Geometric Data Analysis by Brigitte Le Roux,Henry Rouanet Pdf

Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzécri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. Chapter 9, Research Case Studies, is nearly a book in itself; it presents the methodology in action on three extensive applications, one for medicine, one from political science, and one from education (data borrowed from the Stanford computer-based Educational Program for Gifted Youth ). Thus the readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis.

Author : Brian Everitt,Torsten Hothorn
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 54,7 Mb
Release : 2011-04-23
Category : Mathematics
ISBN : 9781441996503

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An Introduction to Applied Multivariate Analysis with R by Brian Everitt,Torsten Hothorn Pdf

The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.

Author : Nickolay Trendafilov,Michele Gallo
Publisher : Springer Nature
Page : 467 pages
File Size : 40,9 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9783030769741

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Multivariate Data Analysis on Matrix Manifolds by Nickolay Trendafilov,Michele Gallo Pdf

This graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization.

Author : David J. Saville,Graham R. Wood
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207474

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Statistical Methods by David J. Saville,Graham R. Wood Pdf

The aim of this book is to present the mathematics underlying elementary statistical methods in as simple a manner as possible. These methods include independent and paired sample t-tests, analysis of variance, regression, and the analysis of covariance. The author's principle tool is the use of geometric ideas to provide more visual insight and to make the theory accessible to a wider audience than is usually possible.

Author : Sean Dineen
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 51,8 Mb
Release : 2001-03-30
Category : Mathematics
ISBN : 185233472X

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Multivariate Calculus and Geometry by Sean Dineen Pdf

This book provides the higher-level reader with a comprehensive review of all important aspects of Differential Calculus, Integral Calculus and Geometric Calculus of several variables The revised edition, which includes additional exercises and expanded solutions, and gives a solid description of the basic concepts via simple familiar examples which are then tested in technically demanding situations. Readers will gain a deep understanding of the uses and limitations of multivariate calculus.

Author : Narayan C. Giri
Publisher : Academic Press
Page : 336 pages
File Size : 40,6 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483263335

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Multivariate Statistical Inference by Narayan C. Giri Pdf

Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling distributions. Chapter III is devoted to basic notions of multivariate distributions and the principle of invariance in statistical testing of hypotheses. Chapters IV and V deal with the study of the real multivariate normal distribution through the probability density function and through a simple characterization and the maximum likelihood estimators of the parameters of the multivariate normal distribution and their optimum properties. Chapter VI tackles a systematic derivation of basic multivariate sampling distributions for the real case, while Chapter VII explores the tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimum properties. Chapter VIII is devoted to a systematic derivation of tests concerning covariance matrices and mean vectors of multivariate normal populations and to the study of their optimum properties. Chapters IX and X look into a treatment of discriminant analysis and the different covariance models and their analysis for the multivariate normal distribution. These chapters also deal with the principal components, factor models, canonical correlations, and time series. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

Author : C.M. Cuadras,C.R. Rao
Publisher : Elsevier
Page : 494 pages
File Size : 54,6 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9781483297569

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Multivariate Analysis: Future Directions 2 by C.M. Cuadras,C.R. Rao Pdf

The contributions in this volume, made by distinguished statisticians in several frontier areas of research in multivariate analysis, cover a broad field and indicate future directions of research. The topics covered include discriminant analysis, multidimensional scaling, categorical data analysis, correspondence analysis and biplots, association analysis, latent variable models, bootstrap distributions, differential geometry applications and others. Most of the papers propose generalizations or new applications of multivariate analysis. This volume will be of great interest to statisticians, probabilists, data analysts and scientists working in the disciplines such as biology, biometry, ecology, medicine, econometry, psychometry and marketing. It will be a valuable guide to professors, researchers and graduate students seeking new and promising lines of statistical research.

Author : Richard A. Johnson,Dean W. Wichern
Publisher : Pearson
Page : 808 pages
File Size : 53,8 Mb
Release : 2018-03-18
Category : Multivariate analysis
ISBN : 0134995392

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Applied Multivariate Statistical Analysis (Classic Version) by Richard A. Johnson,Dean W. Wichern Pdf

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. For courses in Multivariate Statistics, Marketing Research, Intermediate Business Statistics, Statistics in Education, and graduate-level courses in Experimental Design and Statistics. Appropriate for experimental scientists in a variety of disciplines, this market-leading text offers a readable introduction to the statistical analysis of multivariate observations. Its primary goal is to impart the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. Ideal for a junior/senior or graduate level course that explores the statistical methods for describing and analyzing multivariate data, the text assumes two or more statistics courses as a prerequisite.