Linear Model Theory: Exercises and Solutions

✍ Scribed by Dale L. Zimmerman

Publisher: Springer International Publishing;Springer
Year: 2020
Tongue: English
Leaves: 350
Edition: 1st ed.
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-vii
A Brief Introduction (Dale L. Zimmerman)....Pages 1-1
Selected Matrix Algebra Topics and Results (Dale L. Zimmerman)....Pages 3-6
Generalized Inverses and Solutions to Systems of Linear Equations (Dale L. Zimmerman)....Pages 7-19
Moments of a Random Vector and of Linear and Quadratic Forms in a Random Vector (Dale L. Zimmerman)....Pages 21-29
Types of Linear Models (Dale L. Zimmerman)....Pages 31-38
Estimability (Dale L. Zimmerman)....Pages 39-61
Least Squares Estimation for the Gauss–Markov Model (Dale L. Zimmerman)....Pages 63-89
Least Squares Geometry and the Overall ANOVA (Dale L. Zimmerman)....Pages 91-102
Least Squares Estimation and ANOVA for Partitioned Models (Dale L. Zimmerman)....Pages 103-129
Constrained Least Squares Estimation and ANOVA (Dale L. Zimmerman)....Pages 131-152
Best Linear Unbiased Estimation for the Aitken Model (Dale L. Zimmerman)....Pages 153-169
Model Misspecification (Dale L. Zimmerman)....Pages 171-184
Best Linear Unbiased Prediction (Dale L. Zimmerman)....Pages 185-222
Distribution Theory (Dale L. Zimmerman)....Pages 223-253
Inference for Estimable and Predictable Functions (Dale L. Zimmerman)....Pages 255-323
Inference for Variance–Covariance Parameters (Dale L. Zimmerman)....Pages 325-350
Empirical BLUE and BLUP (Dale L. Zimmerman)....Pages 351-353

✦ Subjects

Statistics; Statistical Theory and Methods; Linear and Multilinear Algebras, Matrix Theory

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