Linear Model Theory

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.

• 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.

“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)