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Linear Model Theory: Exercises and Solutions de Dale L. Zimmerman

Linear Model Theory: Exercises and Solutions

Autor Dale L. Zimmerman
en Limba Engleză Hardback – 3 noi 2020
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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Specificații

ISBN-13: 9783030520731
ISBN-10: 3030520730
Pagini: 250
Ilustrații: VII, 353 p. 4 illus.
Dimensiuni: 155 x 235 x 31 mm
Greutate: 0.71 kg
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

1 A Brief Introduction.- 2 Selected Matrix Algebra Topics and Results.- 3 Generalized Inverses and Solutions to Sytems 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.

Recenzii

“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)

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

Presents a unique collection of 296 exercises and complete solutions on linear model theory Covers a wide variety of topics, including best linear unbiased estimation and prediction Will benefit students and instructors alike