Overview
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
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (17 chapters)
-
Front Matter
-
Back Matter
Keywords
- 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
- Gauss-Markov model
- Aitken model
- distribution theory
- mixed and random effects models
- BLUE and BLUP
About this book
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.
Reviews
“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)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Linear Model Theory
Book Subtitle: With Examples and Exercises
Authors: Dale L. Zimmerman
DOI: https://doi.org/10.1007/978-3-030-52063-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-52062-5Published: 03 November 2020
Softcover ISBN: 978-3-030-52065-6Published: 03 November 2021
eBook ISBN: 978-3-030-52063-2Published: 02 November 2020
Edition Number: 1
Number of Pages: XXI, 504
Number of Illustrations: 14 b/w illustrations
Topics: Statistical Theory and Methods, Linear and Multilinear Algebras, Matrix Theory