Linear Model Theory
With Examples and Exercises
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Beschreibung
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 book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.
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 book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.
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
Autor*in
Dale L. Zimmerman
Themen in »Linear Model Theory«
62J05, 62J10, 62F03, 62F10, 62F25 linear models statistical theory regression methods generalized inverse least squares estimation ANOVA best linear unbiased estimation and prediction variance component estimation examples and exercises estimability matrix algebra random vectors model misspecication mean and error structures
Stimmen zu »Linear Model Theory«
“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)
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