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Matrix Algebra Useful for Statistics

Matrix Algebra Useful for Statistics Author Shayle R. Searle
ISBN-10 9781118935149
Release 2017-05
Pages 512
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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.

Matrix Analysis for Statistics

Matrix Analysis for Statistics Author James R. Schott
ISBN-10 9781119092483
Release 2016-06-20
Pages 552
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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.

Matrices for Statistics

Matrices for Statistics Author M. J. R. Healy
ISBN-10 019850702X
Release 2000
Pages 147
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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

Matrix Algebra Author James E. Gentle
ISBN-10 9783319648675
Release 2017-10-12
Pages 648
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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 for Linear Models

Matrix Algebra for Linear Models Author Marvin H. J. Gruber
ISBN-10 9781118608814
Release 2013-12-13
Pages 392
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A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.

A Matrix Handbook for Statisticians

A Matrix Handbook for Statisticians Author George A. F. Seber
ISBN-10 0470226781
Release 2008-01-28
Pages 576
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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.

Matrices with Applications in Statistics

Matrices with Applications in Statistics Author Franklin A. Graybill
ISBN-10 0534401317
Release 2001-12-01
Pages 461
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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.

Matrix Algebra for Applied Economics

Matrix Algebra for Applied Economics Author Shayle R. Searle
ISBN-10 0471322075
Release 2001-09-13
Pages 432
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Coverage of matrix algebra for economists and students of economics Matrix Algebra for Applied Economics explains the important tool of matrix algebra for students of economics and practicing economists. It includes examples that demonstrate the foundation operations of matrix algebra and illustrations of using the algebra for a variety of economic problems. The authors present the scope and basic definitions of matrices, their arithmetic and simple operations, and describe special matrices and their properties, including the analog of division. They provide in-depth coverage of necessary theory and deal with concepts and operations for using matrices in real-life situations. They discuss linear dependence and independence, as well as rank, canonical forms, generalized inverses, eigenroots, and vectors. Topics of prime interest to economists are shown to be simplified using matrix algebra in linear equations, regression, linear models, linear programming, and Markov chains. Highlights include: * Numerous examples of real-world applications * Challenging exercises throughout the book * Mathematics understandable to readers of all backgrounds * Extensive up-to-date reference material Matrix Algebra for Applied Economics provides excellent guidance for advanced undergraduate students and also graduate students. Practicing economists who want to sharpen their skills will find this book both practical and easy-to-read, no matter what their applied interests.

Variance Components

Variance Components Author Shayle R. Searle
ISBN-10 9780470317693
Release 2009-09-25
Pages 501
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WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . .Variance Components is an excellent book. It is organized and well written, and provides many references to a variety of topics. I recommend it to anyone with interest in linear models." —Journal of the American Statistical Association "This book provides a broad coverage of methods for estimating variance components which appeal to students and research workers . . . The authors make an outstanding contribution to teaching and research in the field of variance component estimation." —Mathematical Reviews "The authors have done an excellent job in collecting materials on a broad range of topics. Readers will indeed gain from using this book . . . I must say that the authors have done a commendable job in their scholarly presentation." —Technometrics This book focuses on summarizing the variability of statistical data known as the analysis of variance table. Penned in a readable style, it provides an up-to-date treatment of research in the area. The book begins with the history of analysis of variance and continues with discussions of balanced data, analysis of variance for unbalanced data, predictions of random variables, hierarchical models and Bayesian estimation, binary and discrete data, and the dispersion mean model.

Matrix differential calculus with applications in statistics and econometrics

Matrix differential calculus with applications in statistics and econometrics Author Jan R. Magnus
ISBN-10 0471915165
Release 1988-04-25
Pages 393
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This book provides a unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. Divided into six parts, the book begins with a treatment of matrix algebra, discussing the Schur, Jordan, and singular-value decompositions, the Hadamard and Kronecker products, and more. The second section is the theoretical core of the book and presents a thorough development of the theory of differentials. Practically-oriented, part three contains the rules for working with differentials and lists the differentials of important scalar, vector, and matrix functions. The fourth deals with inequalities, such as Cauchy-Schwarz's and Minkowski's, while the fifth section is devoted to applications of matrix differential calculus to the linear regression model. The book closes by detailing maximum likelihood estimation, an ideal source for demonstrating the power of the propagated techniques. Features numerous exercises.

Linear Models

Linear Models Author Shayle R. Searle
ISBN-10 9781118952856
Release 2016-09-28
Pages 696
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Provides an easy-to-understand guide to statistical linear models and its uses in data analysis This book defines a broad spectrum of statistical linear models that is useful in the analysis of data. Considerable rewriting was done to make the book more reader friendly than the first edition. Linear Models, Second Edition is written in such a way as to be self-contained for a person with a background in basic statistics, calculus and linear algebra. The text includes numerous applied illustrations, numerical examples, and exercises, now augmented with computer outputs in SAS and R. Also new to this edition is: • A greatly improved internal design and format • A short introductory chapter to ease understanding of the order in which topics are taken up • Discussion of additional topics including multiple comparisons and shrinkage estimators • Enhanced discussions of generalized inverses, the MINQUE, Bayes and Maximum Likelihood estimators for estimating variance components Furthermore, in this edition, the second author adds many pedagogical elements throughout the book. These include numbered examples, end-of-example and end-of-proof symbols, selected hints and solutions to exercises available on the book’s website, and references to “big data” in everyday life. Featuring a thorough update, Linear Models, Second Edition includes: • A new internal format, additional instructional pedagogy, selected hints and solutions to exercises, and several more real-life applications • Many examples using SAS and R with timely data sets • Over 400 examples and exercises throughout the book to reinforce understanding Linear Models, Second Edition is a textbook and a reference for upper-level undergraduate and beginning graduate-level courses on linear models, statisticians, engineers, and scientists who use multiple regression or analysis of variance in their work. SHAYLE R. SEARLE, PhD, was Professor Emeritus of Biometry at Cornell University. He was the author of the first edition of Linear Models, Linear Models for Unbalanced Data, and Generalized, Linear, and Mixed Models (with Charles E. McCulloch), all from Wiley. The first edition of Linear Models appears in the Wiley Classics Library. MARVIN H. J. GRUBER, PhD, is Professor Emeritus at Rochester Institute of Technology, School of Mathematical Sciences. Dr. Gruber has written a number of papers and has given numerous presentations at professional meetings during his tenure as a professor at RIT. His fields of interest include regression estimators and the improvement of their efficiency using shrinkage estimators. He has written and published two books on this topic. Another of his books, Matrix Algebra for Linear Models, also published by Wiley, provides good preparation for studying Linear Models. He is a member of the American Mathematical Society, the Institute of Mathematical Statistics and the American Statistical Association.

Applied Regression Analysis

Applied Regression Analysis Author Norman R. Draper
ISBN-10 9781118625682
Release 2014-08-25
Pages 736
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An outstanding introduction to the fundamentals of regression analysis-updated and expanded The methods of regression analysis are the most widely used statistical tools for discovering the relationships among variables. This classic text, with its emphasis on clear, thorough presentation of concepts and applications, offers a complete, easily accessible introduction to the fundamentals of regression analysis. Assuming only a basic knowledge of elementary statistics, Applied Regression Analysis, Third Edition focuses on the fitting and checking of both linear and nonlinear regression models, using small and large data sets, with pocket calculators or computers. This Third Edition features separate chapters on multicollinearity, generalized linear models, mixture ingredients, geometry of regression, robust regression, and resampling procedures. Extensive support materials include sets of carefully designed exercises with full or partial solutions and a series of true/false questions with answers. All data sets used in both the text and the exercises can be found on the companion disk at the back of the book. For analysts, researchers, and students in university, industrial, and government courses on regression, this text is an excellent introduction to the subject and an efficient means of learning how to use a valuable analytical tool. It will also prove an invaluable reference resource for applied scientists and statisticians.

Advanced Calculus with Applications in Statistics

Advanced Calculus with Applications in Statistics Author André I. Khuri
ISBN-10 9780471461623
Release 2003-04-14
Pages 704
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Designed to help motivate the learning of advanced calculus by demonstrating its relevance in the field of statistics, this successful text features detailed coverage of optimization techniques and their applications in statistics while introducing the reader to approximation theory. The Second Edition provides substantial new coverage of the material, including three new chapters and a large appendix that contains solutions to almost all of the exercises in the book. Applications of some of these methods in statistics are discusses.

Applications of Statistics to Industrial Experimentation

Applications of Statistics to Industrial Experimentation Author Cuthbert Daniel
ISBN-10 9780470317174
Release 2009-09-25
Pages 320
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Other volumes in the Wiley Series in Probability and Mathematical Statistics, Ralph A. Bradley, J. Stuart Hunter, David G. Kendall, & Geoffrey S. Watson, Advisory Editors Statistical Models in Applied Science Karl V. Bury Of direct interest to engineers and applied scientists, this book presents general principles of statistics and specific distribution methods and models. Prominent distribution properties and methods that are useful over a wide range of applications are covered in detail. The strengths and weaknesses of the distributional models are fully described, giving the reader a firm, intuitive approach to the selection of the model most appropriate to the problem at hand. 1975 656 pp. Fitting Equations To Data Computer Analysis of Multifactor Data for Scientists and Engineers Cuthbert Daniel & Fred S. Wood With the assistance of John W. Gorman The purpose of this book is to help the serious data analyst, scientist, or engineer with a computer to: recognize the strengths and limitations of his data; test the assumptions implicit in the least squares methods used to fit the data; select appropriate forms of the variables; judge which combinations of variables are most influential; and state the conditions under which the fitted equations are applicable. Throughout, mathematics is kept at the level of college algebra. 1971 342 pp. Methods for Statistical Analysis of Reliability And Life Data Nancy R. Mann, Ray E. Schafer & Nozer D. Singpurwalla This book introduces failure models commonly used in reliability analysis, and presents the most useful methods for analyzing the life data of these models. Highlights include: material on accelerated life testing; a comprehensive treatment of estimation and hypothesis testing; a critical survey of methods for system-reliability confidence bonds; and methods for simulation of life data and for testing fit. 1974 564 pp.

Introductory Mathematics and Statistics for Islamic Finance

Introductory Mathematics and Statistics for Islamic Finance Author Abbas Mirakhor
ISBN-10 9781118779729
Release 2014-06-10
Pages 256
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A unique primer on quantitative methods as applied to Islamic finance Introductory Mathematics and Statistics for Islamic Finance + Website is a comprehensive guide to quantitative methods, specifically as applied within the realm of Islamic finance. With applications based on research, the book provides readers with the working knowledge of math and statistics required to understand Islamic finance theory and practice. The numerous worked examples give students with various backgrounds a uniform set of common tools for studying Islamic finance. The in-depth study of finance requires a strong foundation in quantitative methods. Without a good grasp of math, probability, and statistics, published theoretical and applied works in Islamic finance remain out of reach. Unlike a typical math text, this book guides students through only the methods that directly apply to Islamic finance, without wasting time on irrelevant techniques. Each chapter contains a detailed explanation of the topic at hand, followed by an example based on real situations encountered in Islamic finance. Topics include: Algebra and matrices Calculus and differential equations Probability theory Statistics Written by leading experts on the subject, the book serves as a useful primer on the analysis methods and techniques students will encounter in published research, as well as day-to-day operations in finance. Anyone aspiring to be successful in Islamic finance needs these skills, and Introductory Mathematics and Statistics for Islamic Finance + Website is a clear, concise, and highly relevant guide.

Linear Models in Statistics

Linear Models in Statistics Author Alvin C. Rencher
ISBN-10 9780470192603
Release 2008-01-18
Pages 688
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The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.

A User s Guide to Principal Components

A User s Guide to Principal Components Author J. Edward Jackson
ISBN-10 9780471725329
Release 2005-01-21
Pages 592
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WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of A User’s Guide to Principal Components "The book is aptly and correctly named–A User’s Guide. It is the kind of book that a user at any level, novice or skilled practitioner, would want to have at hand for autotutorial, for refresher, or as a general-purpose guide through the maze of modern PCA." –Technometrics "I recommend A User’s Guide to Principal Components to anyone who is running multivariate analyses, or who contemplates performing such analyses. Those who write their own software will find the book helpful in designing better programs. Those who use off-the-shelf software will find it invaluable in interpreting the results." –Mathematical Geology