The Geometry Of Multivariate Statistics


The Geometry Of Multivariate Statistics
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The Geometry Of Multivariate Statistics


The Geometry Of Multivariate Statistics
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Author : Thomas D. Wickens
language : en
Publisher: Psychology Press
Release Date : 2014-02-25

The Geometry Of Multivariate Statistics written by Thomas D. Wickens and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-25 with Psychology categories.


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


Data Depth
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Author : Regina Y. Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Data Depth written by Regina Y. Liu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Geometry categories.


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).



Applied Multivariate Statistical Analysis


Applied Multivariate Statistical Analysis
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Author : Richard A. Johnson
language : en
Publisher:
Release Date : 2006

Applied Multivariate Statistical Analysis written by Richard A. Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.




Multivariate Calculus And Geometry


Multivariate Calculus And Geometry
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Author : Sean Dineen
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03-30

Multivariate Calculus And Geometry written by Sean Dineen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-30 with Mathematics categories.


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.



Mathematical Tools For Applied Multivariate Analysis


Mathematical Tools For Applied Multivariate Analysis
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Author : Paul E. Green
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Mathematical Tools For Applied Multivariate Analysis written by Paul E. Green and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.


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 Calculus And Geometry


Multivariate Calculus And Geometry
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Author : Seán Dineen
language : en
Publisher: Springer
Release Date : 2014-09-18

Multivariate Calculus And Geometry written by Seán Dineen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-18 with Mathematics categories.


Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.



Applied Multivariate Statistical Analysis


Applied Multivariate Statistical Analysis
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Author : Wolfgang Karl Härdle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Applied Multivariate Statistical Analysis written by Wolfgang Karl Härdle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.


A state of the art presentation of the tools and concepts of multivariate data analysis with a strong focus on applications. The first part is devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents distributions, estimators and tests for various practical situations. The last part covers mulivariate techniques and introduces the reader into the wide variety of tools for multivariate data analysis. The text presents a wide range of examples and 228 exercises.



Theory Of Multivariate Statistics


Theory Of Multivariate Statistics
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Author : Martin Bilodeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-20

Theory Of Multivariate Statistics written by Martin Bilodeau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-20 with Mathematics categories.


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.



Geometric Data Analysis


Geometric Data Analysis
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Author : Brigitte Le Roux
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16

Geometric Data Analysis written by Brigitte Le Roux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.


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.



Geometry Driven Statistics


Geometry Driven Statistics
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Author : Ian L. Dryden
language : en
Publisher: John Wiley & Sons
Release Date : 2015-09-03

Geometry Driven Statistics written by Ian L. Dryden and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Mathematics categories.


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.