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Author: Thomas D. Wickens
Publisher: Psychology Press
ISBN: 1317780221
Category : Psychology
Languages : en
Pages : 216
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Book Description
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: Thomas D. Wickens
Publisher: Psychology Press
ISBN: 1317780221
Category : Psychology
Languages : en
Pages : 216
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Book Description
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: Martin Bilodeau
Publisher: Springer Science & Business Media
ISBN: 0387226168
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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
ISBN: 1483214044
Category : Mathematics
Languages : en
Pages : 391
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Book Description
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: Ian L. Dryden
Publisher: John Wiley & Sons
ISBN: 1118866606
Category : Mathematics
Languages : en
Pages : 436
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Book Description
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:
ISBN:
Category : Mathematics
Languages : en
Pages : 528
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Book Description
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: Sean Dineen
Publisher: Springer Science & Business Media
ISBN: 9781852334727
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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: David J. Saville
Publisher: Springer Science & Business Media
ISBN: 1461207479
Category : Mathematics
Languages : en
Pages : 279
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Book Description
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: David J. Bartholomew
Publisher: CRC Press
ISBN: 1584889616
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Drawing on the authors' varied experiences working and teaching in the field, Analysis of Multivariate Social Science Data, Second Editionenables a basic understanding of how to use key multivariate methods in the social sciences. With updates in every chapter, this edition expands its topics to include regression analysis, con
Author: Nickolay Trendafilov
Publisher: Springer Nature
ISBN: 3030769747
Category : Mathematics
Languages : en
Pages : 467
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Book Description
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: Brian Everitt
Publisher: Springer Science & Business Media
ISBN: 1441996508
Category : Mathematics
Languages : en
Pages : 284
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Book Description
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.
