Matrices for Statistics

Author: M. J. R. Healy
Publisher: Oxford University Press
ISBN: 9780198507024
Format: PDF, ePub, Docs
Download Now
Multiple regression, linear modelling, and multivariate analysis are among the most useful statistical methods for the elucidation of complicated data, and all of them are most easily explained in matrix terms. Anyone concerned with the analysis of data needs to be familiar with these methods and a knowledge of matrices is essential in order to understand the literature in which they are described. This knowledge must include some advanced topics, but can do without much of the material covered by general textbooks of matrix algebra. This book is intended to cover the necessary ground as briefly as possible. Only the simplest of basic mathematics is used, and the book should be accessible to engineers, biologists, and social scientists as well as those with a specifically mathematical background. The text of the first edition has been re-written and revised to take account of recent developments in statistical practice. The more difficult topics have been expanded and the mathematical explanations have been simplified. A new chapter has been included, at readers' request, to cover such topics as vectorising, matrix calculus and complex numbers. From the reviews of the first edition '...this should be a valuable handbook for a great variety of statistical users.' Short Book Reviews of the International Statistics Institute '...a good reference book for the serious student.' Journal of the American Statistical Association '...a very worthwhile addition to anyone's shelf. Teaching Statistics 'I recommend it.' Technometrics

Matrix Algebra

Author: James E. Gentle
Publisher: Springer
ISBN: 3319648675
Format: PDF, ePub, Docs
Download Now
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Linear Algebra and Matrix Analysis for Statistics

Author: Sudipto Banerjee
Publisher: CRC Press
ISBN: 1420095382
Format: PDF, ePub
Download Now
Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Matrix Analysis for Statistics

Author: James R. Schott
Publisher: John Wiley & Sons
ISBN: 1119092485
Format: PDF, ePub, Docs
Download Now
An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

Matrices with Applications in Statistics

Author: Franklin A. Graybill
Publisher: Duxbury Press
ISBN: 9780534401313
Format: PDF, ePub, Docs
Download Now
Part of the Duxbury Classic series, Franklin A. Graybill’s MATRICES WITH APPLICATIONS TO STATISTICS focuses primarily on matrices as they relate to areas of multivariate analysis and the linear model. This seminal work is a time tested, authoritative resource for both students and researchers.

Advanced Multivariate Statistics with Matrices

Author: Tõnu Kollo
Publisher: Springer Science & Business Media
ISBN: 1402034199
Format: PDF
Download Now
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.

Matrix Algebra Useful for Statistics

Author: Shayle R. Searle
Publisher: John Wiley & Sons
ISBN: 1118935144
Format: PDF, ePub, Mobi
Download Now
This book addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of SAS, MATLAB, and R for the execution of matrix computations.

Basics of Matrix Algebra for Statistics with R

Author: Nick Fieller
Publisher: CRC Press
ISBN: 149871238X
Format: PDF, ePub, Docs
Download Now
A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.

Matrix Algebra and Its Applications to Statistics and Econometrics

Author: Calyampudi Radhakrishna Rao
Publisher: World Scientific
ISBN: 9789810232689
Format: PDF, Kindle
Download Now
"I recommend this book for its extensive coverage of topics not easily found elsewhere and for its focus on applications".Zentralblatt MATH"The book is an excellent source on linear algebra, matrix theory and applications in statistics and econometrics, and is unique in many ways. I recommend it to anyone interested in these disciplines, and especially in how they benefit from one another".Statistical Papers, 2000