A First Course in Linear Model Theory

Cover Page
Table of Contents
Ch. 1 Review of Vector and Matrix Algebra
	1.2 Basic definitions and properties
	Exercises
Ch. 2 Properties of Special Matrices
	2.1 Partitioned Matrices
	2.2 Algorithms for matrix factorization
	2.3 Symmetric and idempotent matrices
	2.4 Nonnegative definite quadritic forms and matrices
	2.5 Simultaneous diagonalization of matrices
	2.6 Geometrical Perspectives
	2.7 Vector and matrix differentiation
	2.8 Special operations on matrices
	2.9 Linear optimization
	Exercises
Ch. 3 Generalized Inverses and Solutions to Linear Systems
	3.1 Generalized inverses
	3.2 Solutions to linear systems
	Exercises
Ch. 4 The General Linear Model
	4.1 Model definition and examples
	4.2 The least squares approach
	4.3 Estimable functions
	4.4 Gauss-Markov theorem
	4.5 Generalized least squares
	4.6 Estimation subject to linear restrictions
	Exercises
Ch. 5 Multivariate Normal and Related Distributions
	5.1 Multivariate probability distributions
	5.2 Multivariate normal distribution and properties
	5.3 Some noncentral distributions
	5.4 Distributions of quadratic forms
	5.5 Alternatives to multivariate normal distribution
	Exercises
Ch. 6 Sampling from the Multivariate Normal Distribution
	6.1 Distribution of sample mean and covariance
	6.2 Distributions related to correlation coefficients
	6.3 Assessing the normality assumption
	6.4 Transformations to approximate normality
	Exercises
Ch. 7 Inference for the General Linear Model
	7.1 Properties of least square estimates
	7.2 General linear hypothesis
	7.3 Confidence intervals and multiple comparisons
	7.4 Restricted and reduced models
	7.5 Likelihood based approaches
	Exercises
Ch. 8 Multiple Regression Models
	8.1 Departures from model assumptions
	8.2 Model selection in regression
	8.3 Orthogonal and collinear predictors
	8.4 Prediction intervals and calibration
	8.5 Regression diagnostics
	8.6 Dummy variables in regression
	8.7 Robust regression
	8.8 Nonparametric regression methods
	Exercises
Ch. 9 Fixed Effects Linear Models
	9.1 Checking model assumptions
	9.2 Inference for unbalanced ANOVA models
	9.3 Analaysis of Covariance
	9.4 Nonparametric procedures
	Exercises
Ch. 10 Random-Effects and Mixed-Effects Models
	10.1 One-factor random-effects model
	10.2 Mixed-effects linear models
	Exercises
Ch. 11 Special Topics
	11.1 Bayesian linear models
	11.2 Dynamic linear models
	11.3 Longitudinal models
	11.4 Generalized linear models
	Exercises
A Review of Probability Distributions
Solutions to Selected Exercises
References
Author Index
Subject Index