Linear Model Theory

Exercises and Solutions

2020
Buch

Verfasst von: Dale L. Zimmerman
Verlag: Springer International Publishing
Enthalten in: Springer Professional "Wirtschaft+Technik"; Springer Professional "Technik"; Springer Professional "Wirtschaft"

Über dieses Buch

Dieses Buch enthält 296 Übungen und Lösungen zu einer Vielzahl von Themen der linearen Modelltheorie, darunter generalisierte Inversen, Schätzbarkeit, beste lineare unvoreingenommene Schätzung und Vorhersage, ANOVA, Konfidenzintervalle, simultane Konfidenzintervalle, Hypothesentests und Varianzkomponentenschätzung. Zu den abgedeckten Modellen gehören die Modelle Gauß-Markov und Aitken, gemischte und zufällige Effekte sowie das allgemeine gemischte lineare Modell. Angesichts seines Inhalts wird das Buch für Studenten und Dozenten gleichermaßen nützlich sein. Der Leser kann auch das begleitende Lehrbuch Linear Model Theory - With Examples and Exercises desselben Autors für die Theorie hinter den Übungen konsultieren.

Mit KI übersetzt

Inhaltsverzeichnis

Frontmatter

1. A Brief Introduction

Abstract

This book contains 296 solved exercises on the theory of linear models. The exercises are taken from the author’s graduate-level textbook, Linear Model Theory: With Examples and Exercises, which was published by Springer in 2020. The exercises themselves have been restated, when necessary and feasible, to make them as comprehensible as possible independently of the textbook, but the solutions refer liberally to theorems and other results therein. They are arranged in chapters, the numbers and titles of which are identical to those of the chapters in the textbook that have exercises.

Dale L. Zimmerman

2. Selected Matrix Algebra Topics and Results

Abstract

This chapter presents exercises on selected matrix algebra topics and results and provides solutions to those exercises.

Dale L. Zimmerman

3. Generalized Inverses and Solutions to Systems of Linear Equations

Abstract

This chapter presents exercises on generalized inverses and solutions to systems of linear equations, and provides solutions to those exercises.

Dale L. Zimmerman

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

Abstract

This chapter presents exercises on moments of a random vector and linear and quadratic forms in a random vector and provides solutions to those exercises.

Dale L. Zimmerman

5. Types of Linear Models

Abstract

This chapter presents exercises on types of linear models, and provides solutions to those exercises.

Dale L. Zimmerman

6. Estimability

Abstract

This chapter presents exercises on estimability of linear functions of β in linear models, and provides solutions to those exercises.

Dale L. Zimmerman

7. Least Squares Estimation for the Gauss–Markov Model

Abstract

This chapter presents exercises on least squares estimation for the Gauss–Markov model, and provides solutions to those exercises.

Dale L. Zimmerman

8. Least Squares Geometry and the Overall ANOVA

Abstract

This chapter presents exercises on least squares geometry and the overall analysis of variance, and provides solutions to those exercises.

Dale L. Zimmerman

9. Least Squares Estimation and ANOVA for Partitioned Models

Abstract

This chapter presents exercises on least squares estimation and ANOVA for partitioned linear models and provides solutions to those exercises.

Dale L. Zimmerman

10. Constrained Least Squares Estimation and ANOVA

Abstract

This chapter presents exercises on least squares estimation and ANOVA for constrained linear models and provides solutions to those exercises.

Dale L. Zimmerman

11. Best Linear Unbiased Estimation for the Aitken Model

Abstract

This chapter presents exercises on best linear unbiased estimation for the Aitken model and provides solutions to those exercises.

Dale L. Zimmerman

12. Model Misspecification

Abstract

This chapter presents exercises on the effects of misspecifying the linear model and provides solutions to those exercises.

Dale L. Zimmerman

13. Best Linear Unbiased Prediction

Abstract

This chapter presents exercises on best linear unbiased prediction under a linear model, and provides solutions to those exercises.

Dale L. Zimmerman

14. Distribution Theory

Abstract

This chapter presents exercises on distribution theory relevant to linear models, and provides solutions to those exercises.

Dale L. Zimmerman

15. Inference for Estimable and Predictable Functions

Abstract

This chapter presents exercises on inference for estimable and predictable functions in linear models and provides solutions to those exercises.

Dale L. Zimmerman

16. Inference for Variance–Covariance Parameters

Abstract

This chapter presents exercises on inference for the variance–covariance parameters of a linear model and provides solutions to those exercises.

Dale L. Zimmerman

17. Empirical BLUE and BLUP

Abstract

This chapter presents exercises on empirical best linear unbiased estimation and empirical best linear unbiased prediction and provides solutions to those exercises.

Dale L. Zimmerman

Metadaten
Barrierefreiheit

Titel: Linear Model Theory
Verfasst von: Dale L. Zimmerman
Verlag: Springer International Publishing
Electronic ISBN: 978-3-030-52074-8
Print ISBN: 978-3-030-52073-1
DOI: https://doi.org/10.1007/978-3-030-52074-8

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Linear Model Theory

Exercises and Solutions

Über dieses Buch

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

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

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