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Tables of Contents for A First Course in Linear Model Theory
A Review of Vector and Matrix Algebra
1
32
Basic definitions and properties
3
30
28
5
Properties of Special Matrices
33
40
Algorithms for matrix factorization
40
5
Symmetric and idempotent matrices
45
6
Nonnegative definite quadratic forms and matrices
51
6
Simultaneous diagonalization of matrices
57
1
Geometrical perspectives
58
5
Vector and matrix differentiation
63
3
Special operations on matrices
66
3
70
3
Generalized Inverses and Solutions to Linear Systems
73
18
Solutions to linear systems
82
9
88
3
The General Linear Model
91
46
Model definition and examples
91
5
The least squares approach
96
17
Generalized least squares
122
7
Estimation subject to linear restrictions
129
8
129
2
Method of orthogonal projections131
2
Exercises133
4
Multivariate Normal and Related Distributions
137
58
Multivariate probability distributions
137
8
Multivariate normal distribution and properties
145
19
Some noncentral distributions
164
8
Distributions of quadratic forms
172
9
Alternatives to the multivariate normal distribution
181
14
181
3
Spherical distributions184
1
Elliptical distributions185
5
Exercises190
5
Sampling from the Multivariate Normal Distribution
195
20
Distribution of the sample mean and covariance matrix
195
5
Distributions related to correlation coefficients
200
4
Assessing the normality assumption
204
5
Transformations to approximate normality
209
6
209
2
Multivariate transformations211
1
Exercises212
3
Inference for the General Linear Model
215
66
Properties of least squares estimates
215
4
General linear hypotheses
219
14
219
12
Power of the F-test231
1
Testing independent and orthogonal contrasts232
1
Confidence intervals and multiple comparisons
233
13
233
3
Simultaneous confidence intervals236
3
Multiple comparison procedures239
7
Restricted and reduced models
246
20
246
17
Lack of fit test263
3
Non-testable hypotheses266
1
Likelihood based approaches
266
15
267
2
Elliptically contoured linear model269
1
Model selection criteria270
1
Other types of likelihood analyses271
6
Exercises277
4
Multiple Regression Models
281
76
Departures from model assumptions
281
15
282
3
Sequential and partial F-tests285
2
Heteroscedasticity287
4
Serial correlation291
4
Stochastic X matrix295
1
Model selection in regression
296
8
Orthogonal and collinear predictors
304
10
304
3
Multicollinearity307
2
Ridge regression309
4
Principal components regression313
1
Prediction intervals and calibration
314
5
Regression diagnostics
319
17
320
1
Types of residuals321
4
Outliers and high leverage observations325
1
Diagnostic measures based on influence functions326
10
Dummy variables in regression
336
3
340
3
M-regression343
1
Nonparametric regression methods
344
13
345
2
Projection pursuit regression347
1
Neural networks regression348
2
Curve estimation based on wavelet methods350
3
Exercises353
4
Fixed Effects Linear Models
357
28
Checking model assumptions
357
2
Inference for unbalanced ANOVA models
359
12
361
2
Higher-order overparametrized models363
8
Analysis of covariance
371
7
Nonparametric procedures
378
7
379
2
Friedman's procedure381
1
Exercises381
4
Random-Effects and Mixed-Effects Models
385
22
One-factor random-effects model
385
10
388
4
Maximum likelihood estimation392
3
Restricted maximum likelihood (REML) estimation395
1
Mixed-effects linear models
395
12
396
2
Estimation procedures398
6
Exercises404
3
Bayesian linear models
407
4
Dynamic linear models
411
5
412
3
Kalman smoothing equations415
1
Multivariate models417
3
Two-stage random-effects models420
2
Generalized linear models
422
11
422
2
Estimation approaches424
4
Residuals and model checking428
2
Generalized additive models430
1
Exercises431
2
A Review of Probability Distributions
433
8
Solutions to Selected Exercises
441
8