The Geometry of Multivariate Statistics

Author: Thomas D. Wickens
Publisher: Psychology Press
ISBN: 9781317780236
Release Date: 2014-02-25
Genre: Psychology

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.

Data Depth

Author: Regina Y. Liu
Publisher: American Mathematical Soc.
ISBN: 0821871129
Release Date:
Genre: Mathematics

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 ofthe 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 theAssociation for Computer Machinery (ACM).

Theory of Multivariate Statistics

Author: Martin Bilodeau
Publisher: Springer Science & Business Media
ISBN: 9780387226163
Release Date: 2008-01-20
Genre: Mathematics

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.

Applied Multivariate Statistical Analysis

Author: Richard Arnold Johnson
Publisher:
ISBN: 013834194X
Release Date: 1998-01-01
Genre: Mathematics

This market leading text provides experimental scientists in a wide variety of disciplines with a readable introduction to the statistical analysis of multivariate observations. Its overarching goal is to provide readers with the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. The Fourth Edition has been revised to take greater advantage of graphical displays of multivariate data and of statistical software programs that facilitate the analysis of complex data. *NEW - Graphical displays of multivariate data moved from Chapter 12 to chapter 1 and many new illustrations and graphics have been added to provide a more visual approach to the subject. *NEW - discussions of important topics including: - Detecting Outliers and Data Cleaning in Chapter 4.- Multivariate Quality Control in Chapter 5. - Monitoring Quality with Principal Components in Chapter 8.- Correspondence Analysis, Biplots, and Procrustes Analysis in Chapter 12. *NEW - Expanded coverage of the following topics: Generalized variance, Assessing normality and transformations to normality, Repeated measures designs, Model checking and other aspects of regre

Mathematical Tools for Applied Multivariate Analysis

Author: Paul E. Green
Publisher: Academic Press
ISBN: 9781483214047
Release Date: 2014-05-10
Genre: Mathematics

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.

Geometric Data Analysis

Author: Brigitte Le Roux
Publisher: Springer Science & Business Media
ISBN: 1402022360
Release Date: 2006-01-16
Genre: Mathematics

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.

Modern Multivariate Statistical Techniques

Author: Alan J. Izenman
Publisher: Springer Science & Business Media
ISBN: 0387781897
Release Date: 2009-03-02
Genre: Mathematics

This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.

Multivariate Statistical Simulation

Author: Mark E. Johnson
Publisher: John Wiley & Sons
ISBN: 0471822906
Release Date: 1987-02-04
Genre: Mathematics

Provides state-of-the-art coverage for the researcher confronted with designing and executing a simulation study using continuous multivariate distributions. Concise writing style makes the book accessible to a wide audience. Well-known multivariate distributions are described, emphasizing a few representative cases from each distribution. Coverage includes Pearson Types II and VII elliptically contoured distributions, Khintchine distributions, and the unifying class for the Burr, Pareto, and logistic distributions. Extensively illustrated--the figures are unique, attractive, and reveal very nicely what distributions ``look like.'' Contains an extensive and up-to-date bibliography culled from journals in statistics, operations research, mathematics, and computer science.

Multivariate Analysis Future Directions 2

Author: C.M. Cuadras
Publisher: Elsevier
ISBN: 9781483297569
Release Date: 2014-05-21
Genre: Mathematics

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.

Advanced Multivariate Statistics with Matrices

Author: Tõnu Kollo
Publisher: Springer Science & Business Media
ISBN: 9781402034190
Release Date: 2006-03-30
Genre: Mathematics

The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.

Discrete Multivariate Analysis

Author: Yvonne M. Bishop
Publisher: Springer Science & Business Media
ISBN: 9780387728063
Release Date: 2007-07-31
Genre: Mathematics

“A welcome addition to multivariate analysis. The discussion is lucid and very leisurely, excellently illustrated with applications drawn from a wide variety of fields. A good part of the book can be understood without very specialized statistical knowledge. It is a most welcome contribution to an interesting and lively subject.” -- Nature Originally published in 1974, this book is a reprint of a classic, still-valuable text.

Geometric Morphometrics for Biologists

Author: Miriam Zelditch
Publisher: Academic Press
ISBN: 0127784608
Release Date: 2004
Genre: Science

Geometric Morphometrics for Biologists is an introductory textbook for a course on geometric morphometrics, written for graduate students and upper division undergraduates, covering both theory of shape analysis and methods of multivariate analysis. It is designed for students with minimal math background; taking them from the process of data collection through basic and more advanced statistical analyses. Many examples are given, beginning with simple although realistic case-studies, through examples of complex analyses requiring several different kinds of methods. The book also includes URL's for free software and step-by-step instructions for using the software. * Accessible, student-tested introduction to sophisticated methods of biological shape analysis * Detailed instructions for conducting analyses with freely available, easy to use software * Numerous illustrations; including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results * Many realistic examples, both simple and complex, from on-going research * Comprehensive glossary of technical terms

Applied Multivariate Statistical Analysis

Author: Richard A. Johnson
Publisher:
ISBN: UCSD:31822023742943
Release Date: 1992
Genre: Analyse multivariée

Explores the statistical methods for describing and analyzing multivariate data. It's goal is to provide readers with the knowledge necessary to make proper interpretations, and select appropriate techniques for analyzing multivariate data Coverage includes: Detecting Outliers and Data Cleaning; Multivariate Quality Control; Monitoring Quality with Principal Components; and Correspondence Analysis, Biplots, and Procrustes Analysis.

Geometry Driven Statistics

Author: Ian L. Dryden
Publisher: John Wiley & Sons
ISBN: 9781118866573
Release Date: 2015-09-28
Genre: Mathematics

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.

Statistics for the 21st Century

Author: Gabor Szekely
Publisher: CRC Press
ISBN: 0824790294
Release Date: 2000-01-25
Genre: Mathematics

A selection of articles presented at the Eighth Lukacs Symposium held at the Bowling Green State University, Ohio. They discuss consistency and accuracy of the sequential bootstrap, hypothesis testing, geometry in multivariate analysis, the classical extreme value model, the analysis of cross-classified data, diffusion models for neural activity, estimation with quadratic loss, econometrics, higher order asymptotics, pre- and post-limit theorems, and more.