Matrix Algebra Useful for Statistics

Author: Shayle R. Searle

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 476

View: 2026

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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. "This book is intended to teach useful matrix algebra to 'students, teachers, consultants, researchers, and practitioners' in 'statistics and other quantitative methods'.The author concentrates on practical matters, and writes in a friendly and informal style . . . this is a useful and enjoyable book to have at hand." -Biometrics This book is an easy-to-understand guide to matrix algebra and its uses in statistical analysis. The material is presented in an explanatory style rather than the formal theorem-proof format. This self-contained text includes numerous applied illustrations, numerical examples, and exercises.

Matrix Analysis for Statistics

Author: James R. Schott

Publisher: John Wiley & Sons

ISBN: 1119092485

Category: Mathematics

Page: 552

View: 6606

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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.

Matrix Algebra for Applied Economics

Author: Shayle R. Searle,Lois Schertz Willett

Publisher: Wiley-Interscience

ISBN: 9780471322078

Category: Mathematics

Page: 432

View: 4860

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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.

Linear Models

Author: Shayle R. Searle,Marvin H. J. Gruber

Publisher: John Wiley & Sons

ISBN: 1118952855

Category: Mathematics

Page: 696

View: 6790

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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 Linear Regression

Author: Sanford Weisberg

Publisher: John Wiley & Sons

ISBN: 1118594851

Category: Mathematics

Page: 368

View: 9523

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Praise for the Third Edition "...this is an excellent book which could easily be used as acourse text..." —International Statistical Institute The Fourth Edition of Applied LinearRegression provides a thorough update of the basic theoryand methodology of linear regression modeling. Demonstrating thepractical applications of linear regression analysis techniques,the Fourth Edition uses interesting, real-worldexercises and examples. Stressing central concepts such as model building, understandingparameters, assessing fit and reliability, and drawing conclusions,the new edition illustrates how to develop estimation, confidence,and testing procedures primarily through the use of least squaresregression. While maintaining the accessible appeal of eachprevious edition,Applied Linear Regression, FourthEdition features: Graphical methods stressed in the initial exploratory phase,analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple andcomplex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, andvariance assumptions Updated methodology, such as bootstrapping, cross-validationbinomial and Poisson regression, and modern model selectionmethods Applied Linear Regression, Fourth Edition is anexcellent textbook for upper-undergraduate and graduate-levelstudents, as well as an appropriate reference guide forpractitioners and applied statisticians in engineering, businessadministration, economics, and the social sciences.

Lineare Algebra

Author: Gilbert Strang

Publisher: Springer-Verlag

ISBN: 3642556310

Category: Mathematics

Page: 656

View: 1813

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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Longitudinal Data Analysis

Author: Donald Hedeker,Robert D. Gibbons

Publisher: John Wiley & Sons

ISBN: 0470036478

Category: Mathematics

Page: 360

View: 309

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Longitudinal data analysis for biomedical and behavioral sciences This innovative book sets forth and describes methods for the analysis of longitudinaldata, emphasizing applications to problems in the biomedical and behavioral sciences. Reflecting the growing importance and use of longitudinal data across many areas of research, the text is designed to help users of statistics better analyze and understand this type of data. Much of the material from the book grew out of a course taught by Dr. Hedeker on longitudinal data analysis. The material is, therefore, thoroughly classroom tested and includes a number of features designed to help readers better understand and apply the material. Statistical procedures featured within the text include: * Repeated measures analysis of variance * Multivariate analysis of variance for repeated measures * Random-effects regression models (RRM) * Covariance-pattern models * Generalized-estimating equations (GEE) models * Generalizations of RRM and GEE for categorical outcomes Practical in their approach, the authors emphasize the applications of the methods, using real-world examples for illustration. Some syntax examples are provided, although the authors do not generally focus on software in this book. Several datasets and computer syntax examples are posted on this title's companion Web site. The authors intend to keep the syntax examples current as new versions of the software programs emerge. This text is designed for both undergraduate and graduate courses in longitudinal data analysis. Instructors can take advantage of overheads and additional course materials available online for adopters. Applied statisticians in biomedicine and the social sciences can also use the book as a convenient reference.

Regression Analysis by Example

Author: Samprit Chatterjee,Ali S. Hadi

Publisher: John Wiley & Sons

ISBN: 0470055456

Category: Mathematics

Page: 416

View: 4040

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The essentials of regression analysis through practical applications Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. This new edition features the following enhancements: Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis A new chapter entitled Further Topics discusses advanced areas of regression analysis Reorganized, expanded, and upgraded exercises appear at the end of each chapter A fully integrated Web page provides data sets Numerous graphical displays highlight the significance of visual appeal Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Random Graphs for Statistical Pattern Recognition

Author: David J. Marchette

Publisher: John Wiley & Sons

ISBN: 9780471722083

Category: Mathematics

Page: 264

View: 3740

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A timely convergence of two widely used disciplines Random Graphs for Statistical Pattern Recognition is the firstbook to address the topic of random graphs as it applies tostatistical pattern recognition. Both topics are of vital interestto researchers in various mathematical and statistical fields andhave never before been treated together in one book. The use ofdata random graphs in pattern recognition in clustering andclassification is discussed, and the applications for bothdisciplines are enhanced with new tools for the statistical patternrecognition community. New and interesting applications for randomgraph users are also introduced. This important addition to statistical literaturefeatures: Information that previously has been available only throughscattered journal articles Practical tools and techniques for a wide range of real-worldapplications New perspectives on the relationship between patternrecognition and computational geometry Numerous experimental problems to encourage practicalapplications With its comprehensive coverage of two timely fields, enhancedwith many references and real-world examples, Random Graphs forStatistical Pattern Recognition is a valuable resource forindustry professionals and students alike.

Robust Statistics

The Approach Based on Influence Functions

Author: Frank R. Hampel,Elvezio M. Ronchetti,Peter J. Rousseeuw,Werner A. Stahel

Publisher: John Wiley & Sons

ISBN: 1118150686

Category: Mathematics

Page: 502

View: 5289

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The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This is a nice book containing a wealth of information, much ofit due to the authors. . . . If an instructor designing such acourse wanted a textbook, this book would be the best choiceavailable. . . . There are many stimulating exercises, and the bookalso contains an excellent index and an extensive list ofreferences." —Technometrics "[This] book should be read carefully by anyone who isinterested in dealing with statistical models in a realisticfashion." —American Scientist Introducing concepts, theory, and applications, RobustStatistics is accessible to a broad audience, avoidingallusions to high-powered mathematics while emphasizing ideas,heuristics, and background. The text covers the approach based onthe influence function (the effect of an outlier on an estimater,for example) and related notions such as the breakdown point. Italso treats the change-of-variance function, fundamental conceptsand results in the framework of estimation of a single parameter,and applications to estimation of covariance matrices andregression parameters.

Time Series

Applications to Finance

Author: Ngai Hang Chan

Publisher: John Wiley & Sons

ISBN: 0471461644

Category: Mathematics

Page: 224

View: 3149

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Elements of Financial Time Series fills a gap in the market in thearea of financial time series analysis by giving both conceptualand practical illustrations. Examples and discussions in the laterchapters of the book make recent developments in time series moreaccessible. Examples from finance are maximized as much as possiblethroughout the book. * Full set of exercises is displayed at the end of eachchapter. * First seven chapters cover standard topics in time series at ahigh-intensity level. * Recent and timely developments in nonstandard time seriestechniques are illustrated with real finance examples indetail. * Examples are systemically illustrated with S-plus with codes anddata available on an associated Web site.

Variance Components

Author: Shayle R. Searle,George Casella,Charles E. McCulloch

Publisher: John Wiley & Sons

ISBN: 0470317698

Category: Mathematics

Page: 501

View: 9288

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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.

Weibull Models

Author: D. N. Prabhakar Murthy,Min Xie,Renyan Jiang

Publisher: John Wiley & Sons

ISBN: 9780471473275

Category: Mathematics

Page: 408

View: 6930

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A comprehensive perspective on Weibull models The literature on Weibull models is vast, disjointed, andscattered across many different journals. Weibull Models is acomprehensive guide that integrates all the different facets ofWeibull models in a single volume. This book will be of great help to practitioners in reliabilityand other disciplines in the context of modeling data sets usingWeibull models. For researchers interested in these modelingtechniques, exercises at the end of each chapter define potentialtopics for future research. Organized into seven distinct parts, Weibull Models: Covers model analysis, parameter estimation, model validation,and application Serves as both a handbook and a research monograph. As ahandbook, it classifies the different models and presents theirproperties. As a research monograph, it unifies the literature andpresents the results in an integrated manner Intertwines theory and application Focuses on model identification prior to model parameterestimation Discusses the usefulness of the Weibull Probability plot (WPP)in the model selection to model a given data set Highlights the use of Weibull models in reliability theory Filled with in-depth analysis, Weibull Models pulls together themost relevant information on this topic to give everyone fromreliability engineers to applied statisticians involved withreliability and survival analysis a clear look at what Weibullmodels can offer.

Applications of Statistics to Industrial Experimentation

Author: Cuthbert Daniel

Publisher: John Wiley & Sons

ISBN: 9780471194699

Category: Mathematics

Page: 294

View: 527

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Simple comparison experiments; Two factors, each at two levels; Two factors, each at three levels; Unreplicated three-factor, two level experiments; Unreplicated four-factor, two-level experiments; Three five-factor, two-level unreplicated experiments; Larger two-way layouts; The size of industrial experiments; Blocking factorial experiments; Fractional replication - elementary; Fractional replication - intermediate; Incomplete factorials; Sequences of fractional replicates; Trend-robust plants; Nested designs.

Handbook of Linear Algebra, Second Edition

Author: Leslie Hogben

Publisher: CRC Press

ISBN: 1498785603

Category: Mathematics

Page: 1904

View: 5724

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With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Theoretical probability for applications

Author: Sidney C. Port

Publisher: Wiley-Interscience

ISBN: 9780471632160

Category: Mathematics

Page: 894

View: 2092

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Offering comprehensive coverage of modern probability theory (exclusive of continuous time stochastic processes), this unique book functions as both an introduction for graduate statisticians, mathematicians, engineers, and economists and an encyclopedic reference of the subject for professionals in these fields. It assumes only a knowledge of calculus as well as basic real analysis and linear algebra. Throughout Theoretical Probability for Applications the focus is on the practical uses of this increasingly important tool. It develops topics of discrete time probability theory for use in a multitude of applications, including stochastic processes, theoretical statistics, and other disciplines that require a sound foundation in modern probability theory. Principles of measure theory related to the study of probability theory are developed as they are required throughout the book. The book examines most of the basic probability models that involve only a finite or countably infinite number of random variables. Topics in the "Discrete Models" section include Bernoulli trials, random walks, matching, sums of indicators, multinomial trials. Poisson approximations and processes, sampling. Markov chains, and discrete renewal theory. Nondiscrete models discussed include univariate, Beta, sampling, and Dirichlet distributions as well as order statistics. A separate chapter covers aspects of the multivariate normal model. Every treatment is carried out for both random vectors and random variables. Consequently, the book contains complete proofs of the vector case which often differ in detail from those of the scalar case. Complete with end-of-chapter exercises that provide both a drill of thematerial presented and an expansion of that same material, explanations of notations used, and a detailed bibliography. Theoretical Probability for Applications is a practical, easy-to-use reference which accommodates the diverse needs of statisticians, mathematicians, economists, engineers, instructors, and students alike.