Matrix Algebra

Theory, Computations and Applications in Statistics
Author: James E. Gentle
Publisher: Springer
ISBN: 3319648675
Category: Mathematics
Page: 648
View: 4438

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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.

Matrix Algebra

Theory, Computations, and Applications in Statistics
Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387708723
Category: Computers
Page: 528
View: 9121

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This much-needed work presents, among other things, the relevant aspects of the theory of matrix algebra for applications in statistics. Written in an informal style, it addresses computational issues and places more emphasis on applications than existing texts.

Matrix Algebra

Theory, Computations, and Applications in Statistics
Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387708731
Category: Mathematics
Page: 530
View: 4062

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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.

Numerical Linear Algebra for Applications in Statistics


Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 1461206235
Category: Mathematics
Page: 221
View: 2125

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Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Linear Algebra and Matrix Analysis for Statistics


Author: Sudipto Banerjee,Anindya Roy
Publisher: CRC Press
ISBN: 1420095382
Category: Mathematics
Page: 580
View: 3975

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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 Algebra: Exercises and Solutions


Author: David A. Harville
Publisher: Springer Science & Business Media
ISBN: 1461301815
Category: Mathematics
Page: 271
View: 9168

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This book contains over 300 exercises and solutions that together cover a wide variety of topics in matrix algebra. They can be used for independent study or in creating a challenging and stimulating environment that encourages active engagement in the learning process. The requisite background is some previous exposure to matrix algebra of the kind obtained in a first course. The exercises are those from an earlier book by the same author entitled Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to stand alone, and the book includes extensive and detailed summaries of all relevant terminology and notation. The coverage includes topics of special interest and relevance in statistics and related disciplines, as well as standard topics. The overlap with exercises available from other sources is relatively small. This collection of exercises and their solutions will be a useful reference for students and researchers in matrix algebra. It will be of interest to mathematicians and statisticians.

Matrix Algebra Useful for Statistics


Author: Shayle R. Searle,Andre I. Khuri
Publisher: John Wiley & Sons
ISBN: 1118935144
Category: Mathematics
Page: 512
View: 6088

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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.

Elements of Computational Statistics


Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387216111
Category: Computers
Page: 420
View: 9455

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Will provide a more elementary introduction to these topics than other books available; Gentle is the author of two other Springer books

Matrix Analysis for Statistics


Author: James R. Schott
Publisher: John Wiley & Sons
ISBN: 1119092485
Category: Mathematics
Page: 552
View: 3503

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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.

Intuitive Introductory Statistics


Author: Douglas A. Wolfe,Grant Schneider
Publisher: Springer
ISBN: 3319560727
Category: Mathematics
Page: 976
View: 7530

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This textbook is designed to give an engaging introduction to statistics and the art of data analysis. The unique scope includes, but also goes beyond, classical methodology associated with the normal distribution. What if the normal model is not valid for a particular data set? This cutting-edge approach provides the alternatives. It is an introduction to the world and possibilities of statistics that uses exercises, computer analyses, and simulations throughout the core lessons. These elementary statistical methods are intuitive. Counting and ranking features prominently in the text. Nonparametric methods, for instance, are often based on counts and ranks and are very easy to integrate into an introductory course.​ The ease of computation with advanced calculators and statistical software, both of which factor into this text, allows important techniques to be introduced earlier in the study of statistics. This book's novel scope also includes measuring symmetry with Walsh averages, finding a nonparametric regression line, jackknifing, and bootstrapping​. Concepts and techniques are explored through practical problems. Quantitative reasoning is at the core of so many professions and academic disciplines, and this book opens the door to the most modern possibilities.

Matrix Algebra


Author: Karim M. Abadir,Jan R. Magnus
Publisher: Cambridge University Press
ISBN: 9780521822893
Category: Business & Economics
Page: 434
View: 1438

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A stand-alone textbook in matrix algebra for econometricians and statisticians - advanced undergraduates, postgraduates and teachers.

Matrices

Theory and Applications
Author: Denis Serre
Publisher: Springer Science & Business Media
ISBN: 9781441976833
Category: Mathematics
Page: 289
View: 897

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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.

A Matrix Handbook for Statisticians


Author: George A. F. Seber
Publisher: John Wiley & Sons
ISBN: 9780470226780
Category: Mathematics
Page: 576
View: 8689

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A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized. A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: Complex matrices A wide range of special matrices and their properties Special products and operators, such as the Kronecker product Partitioned and patterned matrices Matrix analysis and approximation Matrix optimization Majorization Random vectors and matrices Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.

Modern Multivariate Statistical Techniques

Regression, Classification, and Manifold Learning
Author: Alan J. Izenman
Publisher: Springer Science & Business Media
ISBN: 9780387781891
Category: Mathematics
Page: 733
View: 7421

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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.

Numerical Methods in Matrix Computations


Author: Åke Björck
Publisher: Springer
ISBN: 3319050893
Category: Mathematics
Page: 800
View: 4902

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Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Random Number Generation and Monte Carlo Methods


Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 147572960X
Category: Computers
Page: 247
View: 4309

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Monte Carlo simulation has become one of the most important tools in all fields of science. This book surveys the basic techniques and principles of the subject, as well as general techniques useful in more complicated models and in novel settings. The emphasis throughout is on practical methods that work well in current computing environments.

Probability for Statistics and Machine Learning

Fundamentals and Advanced Topics
Author: Anirban DasGupta
Publisher: Springer Science & Business Media
ISBN: 9781441996343
Category: Mathematics
Page: 784
View: 9571

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This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

Statistics and Data Analysis for Financial Engineering

with R examples
Author: David Ruppert,David S. Matteson
Publisher: Springer
ISBN: 1493926144
Category: Business & Economics
Page: 719
View: 8169

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The new edition of this influential textbook, geared towards graduate or advanced undergraduate students, teaches the statistics necessary for financial engineering. In doing so, it illustrates concepts using financial markets and economic data, R Labs with real-data exercises, and graphical and analytic methods for modeling and diagnosing modeling errors. These methods are critical because financial engineers now have access to enormous quantities of data. To make use of this data, the powerful methods in this book for working with quantitative information, particularly about volatility and risks, are essential. Strengths of this fully-revised edition include major additions to the R code and the advanced topics covered. Individual chapters cover, among other topics, multivariate distributions, copulas, Bayesian computations, risk management, and cointegration. Suggested prerequisites are basic knowledge of statistics and probability, matrices and linear algebra, and calculus. There is an appendix on probability, statistics and linear algebra. Practicing financial engineers will also find this book of interest.

An Introduction to Statistical Learning

with Applications in R
Author: Gareth James,Daniela Witten,Trevor Hastie,Robert Tibshirani
Publisher: Springer Science & Business Media
ISBN: 1461471389
Category: Mathematics
Page: 426
View: 1963

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An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform. Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

Matrices with Applications in Statistics


Author: Franklin A. Graybill
Publisher: Duxbury Press
ISBN: 9780534401313
Category: Mathematics
Page: 461
View: 1337

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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.