Download or read book Linear Models in Matrix Form written by Jonathon D. Brown and published by Springer. This book was released on 2015-01-21 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum of squares, the determinant, and the inverse. These operations are explained in everyday language, and their calculations are demonstrated using concrete examples. The remaining chapters build on these operations, progressing from simple linear regression to mediational models with bootstrapped standard errors.
Download or read book Linear Models and the Relevant Distributions and Matrix Algebra written by David A. Harville and published by CRC Press. This book was released on 2023-10-23 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: • Exercises and solutions are included throughout, from both the first and second volume • Includes coverage of additional topics not covered in the first volume • Highly valuable as a reference book for graduate students or researchers
Download or read book Linear Models in Statistics written by Alvin C. Rencher and published by John Wiley & Sons. This book was released on 2008-01-07 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Algebra for Linear Models written by Marvin H. J. Gruber and published by John Wiley & Sons. This book was released on 2013-12-31 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Algebra and Linear Models written by Ravindra B. Bapat and published by Springer Science & Business Media. This book was released on 2008-01-18 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians.
Download or read book A First Course in Linear Model Theory written by Nalini Ravishanker and published by CRC Press. This book was released on 2001-12-21 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding. The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.
Download or read book Linear Models written by Debasis Sengupta and published by World Scientific. This book was released on 2003 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Models: An Integrated Approach aims to provide a clearand deep understanding of the general linear model using simplestatistical ideas. Elegant geometric arguments are also invoked asneeded and a review of vector spaces and matrices is provided to makethe treatment self-contained.
Download or read book Methods and Applications of Linear Models written by Ronald R. Hocking and published by John Wiley & Sons. This book was released on 2005-02-04 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: A popular statistical text now updated and better than ever! The ready availability of high-speed computers and statistical software encourages the analysis of ever larger and more complex problems while at the same time increasing the likelihood of improper usage. That is why it is increasingly important to educate end users in the correct interpretation of the methodologies involved. Now in its second edition, Methods and Applications of Linear Models: Regression and the Analysis of Variance seeks to more effectively address the analysis of such models through several important changes. Notable in this new edition: Fully updated and expanded text reflects the most recent developments in the AVE method Rearranged and reorganized discussions of application and theory enhance text’s effectiveness as a teaching tool More than 100 new exercises in the areas of regression and analysis of variance As in the First Edition, the author presents a thorough treatment of the concepts and methods of linear model analysis, and illustrates them with various numerical and conceptual examples, using a data-based approach to development and analysis. Data sets, available on an FTP site, allow readers to apply analytical methods discussed in the book.
Download or read book A First Course in Linear Model Theory written by Nalini Ravishanker and published by CRC Press. This book was released on 2020-09-14 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation
Download or read book Econometric Methods with Applications in Business and Economics written by Christiaan Heij and published by OUP Oxford. This book was released on 2004-03-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays applied work in business and economics requires a solid understanding of econometric methods to support decision-making. Combining a solid exposition of econometric methods with an application-oriented approach, this rigorous textbook provides students with a working understanding and hands-on experience of current econometrics. Taking a 'learning by doing' approach, it covers basic econometric methods (statistics, simple and multiple regression, nonlinear regression, maximum likelihood, and generalized method of moments), and addresses the creative process of model building with due attention to diagnostic testing and model improvement. Its last part is devoted to two major application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and the econometrics of time series data (univariate time series, trends, volatility, vector autoregressions, and a brief discussion of SUR models, panel data, and simultaneous equations). · Real-world text examples and practical exercise questions stimulate active learning and show how econometrics can solve practical questions in modern business and economic management. · Focuses on the core of econometrics, regression, and covers two major advanced topics, choice data with applications in marketing and micro-economics, and time series data with applications in finance and macro-economics. · Learning-support features include concise, manageable sections of text, frequent cross-references to related and background material, summaries, computational schemes, keyword lists, suggested further reading, exercise sets, and online data sets and solutions. · Derivations and theory exercises are clearly marked for students in advanced courses. This textbook is perfect for advanced undergraduate students, new graduate students, and applied researchers in econometrics, business, and economics, and for researchers in other fields that draw on modern applied econometrics.
Download or read book Linear Models written by Shayle R. Searle and published by John Wiley & Sons. This book was released on 2016-09-28 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Model Theory written by Keith E. Muller and published by John Wiley & Sons. This book was released on 2006-10-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: A precise and accessible presentation of linear model theory, illustrated with data examples Statisticians often use linear models for data analysis and for developing new statistical methods. Most books on the subject have historically discussed univariate, multivariate, and mixed linear models separately, whereas Linear Model Theory: Univariate, Multivariate, and Mixed Models presents a unified treatment in order to make clear the distinctions among the three classes of models. Linear Model Theory: Univariate, Multivariate, and Mixed Models begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation. Data examples motivate and illustrate the models. Chapters 7-10 address distribution theory of multivariate Gaussian variables and quadratic forms. Chapters 11-19 detail methods for estimation, hypothesis testing, and confidence intervals. The final chapters, 20-23, concentrate on choosing a sample size. Substantial sets of excercises of varying difficulty serve instructors for their classes, as well as help students to test their own knowledge. The reader needs a basic knowledge of statistics, probability, and inference, as well as a solid background in matrix theory and applied univariate linear models from a matrix perspective. Topics covered include: A review of matrix algebra for linear models The general linear univariate model The general linear multivariate model Generalizations of the multivariate linear model The linear mixed model Multivariate distribution theory Estimation in linear models Tests in Gaussian linear models Choosing a sample size in Gaussian linear models Filling the need for a text that provides the necessary theoretical foundations for applying a wide range of methods in real situations, Linear Model Theory: Univariate, Multivariate, and Mixed Models centers on linear models of interval scale responses with finite second moments. Models with complex predictors, complex responses, or both, motivate the presentation.
Download or read book Plane Answers to Complex Questions written by Ronald Christensen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of Plane Answers has many additions and a couple of deletions. New material includes additional illustrative examples in Ap pendices A and B and Chapters 2 and 3, as well as discussions of Bayesian estimation, near replicate lack of fit tests, testing the independence assump tion, testing variance components, the interblock analysis for balanced in complete block designs, nonestimable constraints, analysis of unreplicated experiments using normal plots, tensors, and properties of Kronecker prod ucts and Vee operators. The book contains an improved discussion of the relation between ANOVA and regression, and an improved presentation of general Gauss-Markov models. The primary material that has been deleted are the discussions of weighted means and of log-linear models. The mate rial on log-linear models was included in Christensen (1990b), so it became redundant here. Generally, I have tried to clean up the presentation of ideas wherever it seemed obscure to me. Much of the work on the second edition was done while on sabbatical at the University of Canterbury in Christchurch, New Zealand. I would par ticularly like to thank John Deely for arranging my sabbatical. Through their comments and criticisms, four people were particularly helpful in con structing this new edition. I would like to thank Wes Johnson, Snehalata Huzurbazar, Ron Butler, and Vance Berger.
Download or read book Linear Models written by Calyampudi Radhakrishna Rao and published by Springer Science & Business Media. This book was released on 1999 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date account of the theory and applications of linear models. It can be used as a text for courses in statistics at the graduate level as well as an accompanying text for other courses in which linear models play a part. The authors present a unified theory of inference from linear models with minimal assumptions, not only through least squares theory, but also using alternative methods of estimation and testing based on convex loss functions and general estimating equations. The bookincludes a discussion of: -- sensitivity analysis and model selection -- incomplete data sets including regression diagnostics to identify Non-MCAR-processes -- the analysis of categorical data based on a unified presentation of generalized linear models including GEE-methods for correlated response. An extensive appendix on matrix theory will be useful to researchers in econometrics, engineering, and optimization theory.
Download or read book Linear Algebra Done Right written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 1997-07-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Download or read book A SAS IML Companion for Linear Models written by Jamis J. Perrett and published by Springer Science & Business Media. This book was released on 2009-12-21 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear models courses are often presented as either theoretical or applied. Consequently, students may find themselves either proving theorems or using high-level procedures like PROC GLM to analyze data. There exists a gap between the derivation of formulas and analyses that hide these formulas behind attractive user interfaces. This book bridges that gap, demonstrating theory put into practice. Concepts presented in a theoretical linear models course are often trivialized in applied linear models courses by the facility of high-level SAS procedures like PROC MIXED and PROC REG that require the user to provide a few options and statements and in return produce vast amounts of output. This book uses PROC IML to show how analytic linear models formulas can be typed directly into PROC IML, as they were presented in the linear models course, and solved using data. This helps students see the link between theory and application. This also assists researchers in developing new methodologies in the area of linear models. The book contains complete examples of SAS code for many of the computations relevant to a linear models course. However, the SAS code in these examples automates the analytic formulas. The code for high-level procedures like PROC MIXED is also included for side-by-side comparison. The book computes basic descriptive statistics, matrix algebra, matrix decomposition, likelihood maximization, non-linear optimization, etc. in a format conducive to a linear models or a special topics course. Also included in the book is an example of a basic analysis of a linear mixed model using restricted maximum likelihood estimation (REML). The example demonstrates tests for fixed effects, estimates of linear functions, and contrasts. The example starts by showing the steps for analyzing the data using PROC IML and then provides the analysis using PROC MIXED. This allows students to follow the process that lead to the output.
