Linear Model Theory

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About this book

This book contains 296 exercises and solutions covering a wide variety of topics in linear model theory, including generalized inverses, estimability, best linear unbiased estimation and prediction, ANOVA, confidence intervals, simultaneous confidence intervals, hypothesis testing, and variance component estimation. The models covered include the Gauss-Markov and Aitken models, mixed and random effects models, and the general mixed linear model. Given its content, the book will be useful for students and instructors alike. Readers can also consult the companion textbook Linear Model Theory - With Examples and Exercises by the same author for the theory behind the exercises.

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Table of contents (17 chapters)

Front Matter

Pages i-vii

A Brief Introduction

Selected Matrix Algebra Topics and Results

Generalized Inverses and Solutions to Systems of Linear Equations

Moments of a Random Vector and of Linear and Quadratic Forms in a Random Vector

Pages 21-29

Types of Linear Models

Pages 31-38

Estimability

Pages 39-61

Least Squares Estimation for the Gauss–Markov Model

Pages 63-89

Least Squares Geometry and the Overall ANOVA

Pages 91-102

Least Squares Estimation and ANOVA for Partitioned Models

Pages 103-129

Constrained Least Squares Estimation and ANOVA

Pages 131-152

Best Linear Unbiased Estimation for the Aitken Model

Pages 153-169

Model Misspecification

Pages 171-184

Best Linear Unbiased Prediction

Pages 185-222

Distribution Theory

Pages 223-253

Inference for Estimable and Predictable Functions

Pages 255-323

Inference for Variance–Covariance Parameters

Pages 325-350

Empirical BLUE and BLUP

Pages 351-353

Reviews

“This volume contains solutions to the book's exercises … Many of those exercises stand as useful applications of results stated in the theory volume. Some of them go one step beyond and extend the theoretical results. I found this to be a very interesting and unique feature of the book on linear models, making the whole set particularly useful for both graduate students and instructors.” (Vassilis G. S. Vasdekis, Mathematical Reviews, August 2022)

Authors and Affiliations

Department of Statistics and Actuarial Science, University of Iowa, Iowa City, USA

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