Linear Model Theory: With Examples and Exercises by Dale L. Zimmerman (English)

Description: Linear Model Theory by Dale L. Zimmerman This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the books exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author. Back Cover This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the books exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author. Author Biography Dale L. Zimmerman is a Professor at the Department of Statistics and Actuarial Science, University of Iowa, USA. He received his Ph.D. in Statistics from Iowa State University in 1986. A Fellow of the American Statistical Association, his research interests include spatial statistics, longitudinal data analysis, multivariate analysis, mixed linear models, environmental statistics, and sports statistics. He has authored or co-authored three books and more than 90 articles in peer-reviewed journals. At the University of Iowa he teaches courses on linear models, regression analysis, spatial statistics, and mathematical statistics. Table of Contents Preface.- 1 A Brief Introduction.- 2 Selected Matrix Algebra Topics and Results.- 3 Generalized Inverses and Solutions to Systems of Linear Equations.- 4 Moments of a Random Vector and of Linear and Quadratic Forms in a Random Vector.- 5 Types of Linear Models.- 6 Estimability.- 7 Least Squares Estimation for the Gauss-Markov Model.- 8 Least Squares Geometry and the Overall ANOVA.- 9 Least Squares Estimation and ANOVA for Partitioned Models.- 10 Constrained Least Squares Estimation and ANOVA.- 11 Best Linear Unbiased Estimation for the Aitken Model.- 12 Model Misspecification.- 13 Best Linear Unbiased Prediction.- 14 Distribution Theory.- 15 Inference for Estimable and Predictable Functions.- 16 Inference for Variance-Covariance Parameters.- 17 Empirical BLUE and BLUP.- Index. Review "The book presents with great detail the theory needed for estimation of linear functions of model parameters … . The exposition of so many general results for prediction is a significant feature of the book. I also found particularly interesting the detailed presentation of ANOVA formulae … . All these features make the book either a reference one or an excellent textbook for a graduate level course on linear models … ." (Vassilis G. S. Vasdekis, Mathematical Reviews, September, 2022)"This is a classic book to modern linear algebra. It is primarily about linear tranformations and therefore most of the theorems and proofs work for modern linear algebra. The book does start from the beginning and assumes no prior knowledge of the subject. It is also extremely well-written and logical with short and elegant proofs. … The exercises are very good, and are a mixture of proof questions and concrete examples." (Rózsa Horváth-Bokor, zbMATH 1462.62004, 2021) Review Quote "This is a classic book to modern linear algebra. It is primarily about linear tranformations and therefore most of the theorems and proofs work for modern linear algebra. The book does start from the beginning and assumes no prior knowledge of the subject. It is also extremely well-written and logical with short and elegant proofs. ... The exercises are very good, and are a mixture of proof questions and concrete examples." (R Feature Gives as much emphasis to predictive inference as it does to estimation, which is unique for a book on linear models Illustrates every major theorem or concept with at least one special case or example Features a wealth of exercises that will benefit students and instructors alike Presents important elements of linear model methodology as interludes immediately after the respective theoretical content Details ISBN303052065X Author Dale L. Zimmerman Short Title Linear Model Theory Pages 504 Language English Year 2021 ISBN-10 303052065X ISBN-13 9783030520656 Format Paperback Subtitle With Examples and Exercises Publisher Springer Nature Switzerland AG Edition 1st Imprint Springer Nature Switzerland AG Place of Publication Cham Country of Publication Switzerland Publication Date 2021-11-03 UK Release Date 2021-11-03 Illustrations 14 Illustrations, black and white; XXI, 504 p. 14 illus. Edited by Daniel Thalmann Birth 1974 Affiliation Massachusetts Institute of Technology Position journalist Qualifications S. J. Edition Description 1st ed. 2020 Alternative 9783030520625 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:133857086;

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