Linear Models The Theory and Application of

Find a serious approach to the study of linear models and their applications through discussion of analysis of variance (ANOVA) techniques in Linear Models: The Theory and Application of Analysis of Variance. This book represents an equal emphasis on orthogonal representations that delve from the history of the subject and on the vector-matrix approach that has surfaced in recent years. Over 400 exercises varying in degrees of difficulty, orientation and application with some solutions reinforce applications to linear regression (both simple and multiple) and to experimental design.

Brenton R. Clarke, PhD, is Senior Lecturer in Mathematics and Statistics at Murdoch University, Australia. A former president of the Western Australian Branch of the Statistical Society of Australia, Dr. Clarke has published numerous journal articles in his areas of research interest, which include linear models, robust statistics, and time series analysis.

Preface
Acknowledgments
Notation
Introduction
The Linear Model and Examples
What Are the Objectives?
Problems
Projection Matrices and Vector Space Theory
Basis of a Vector Space
Range and Kernel
Projections
Linear Model Application
Sums and Differences of Orthogonal Projections
Problems
Least Squares Theory
The Normal Equations
The Gauss-Markov Theorem
The Distribution of S O
Some Simple Significance Tests
Prediction Intervals
Problems
Distribution Theory
Motivation
Non-Central X 2 and F Distributions
Non-Central F-Distribution
Applications to Linear Models
Some Simple Extensions
Problems
Helmert Matrices and Orthogonal Relationships
Transformations to Independent Normally Distributed Random Variables
The Kronecker Product
Orthogonal Components in Two-Way ANOVA: One Observation Per Cell
Orthogonal Components in Two-Way ANOVA with Replications
The Gauss-Markov Theorem Revisited
Orthogonal Components for Interaction
Testing for Interaction: One Observation Per Cell
Example Calculation of Tukey's One's Degree of Freedom Statistic
Problems
Further Discussion of ANOVA
The Different Representations of Orthogonal Components
On the Lack of Orthogonality
The Relationship Algebra
The Triple Classification
Latin Squares
2 k Factorial Designs
Yates' Algorithm
The Function of Randomization
Brief View of Multiple Comparison Techniques
Problems
Residual Analysis: Diagnostics and Robustness
Design Diagnostics
Standardized and Studentized Residuals
Combining Design and Residual Effects on Fit - DFITS
The Cook-D-Statistic
Robust Approaches
Adaptive Trimmed Likelihood Algorithm
Problems
Models That Include Variance Components
The One-Way Random Effects Model
The Mixed Two-Way Model
A Split Plot Design
A Traditional Model
Problems
Likelihood Approaches
Maximum Likelihood Estimation
REML
Discussion of Hierarchical Statistical Models
Hierarchy for the Mixed Model (Assuming Normality)
Problems
Uncorrelated Residuals Formed from the Linear Model
Best Linear Unbiased Error Estimates
The Best Linear Unbiased Scalar-Covariance-Matrix Approach
Explicit Solution
Recursive Residuals
Recursive Residuals and their Properties
Uncorrelated Residuals
The Main Results
Final Remarks
Problems
Further inferential questions relating to ANOVA
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

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Linear Models The Theory and Application of Analysis of Variance

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Table of Contents

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