Linear Statistical Models, 2nd Edition
August 2009, ©2009
"This impressive and eminently readable text . . . [is] a
welcome addition to the statistical literature."
—The Indian Journal of Statistics
Revised to reflect the current developments on the topic, Linear Statistical Models, Second Edition provides an up-to-date approach to various statistical model concepts. The book includes clear discussions that illustrate key concepts in an accessible and interesting format while incorporating the most modern software applications.
This Second Edition follows an introduction-theorem-proof-examples format that allows for easier comprehension of how to use the methods and recognize the associated assumptions and limits. In addition to discussions on the methods of random vectors, multiple regression techniques, simultaneous confidence intervals, and analysis of frequency data, new topics such as mixed models and curve fitting of models have been added to thoroughly update and modernize the book. Additional topical coverage includes:
An introduction to R and S-Plus® with many examples
Multiple comparison procedures
Estimation of quantiles for regression models
An emphasis on vector spaces and the corresponding geometry
Extensive graphical displays accompany the book's updated descriptions and examples, which can be simulated using R, S-Plus®, and SAS® code. Problems at the end of each chapter allow readers to test their understanding of the presented concepts, and additional data sets are available via the book's FTP site.
Linear Statistical Models, Second Edition is an excellent book for courses on linear models at the upper-undergraduate and graduate levels. It also serves as a comprehensive reference for statisticians, engineers, and scientists who apply multiple regression or analysis of variance in their everyday work.
1 Linear Algebra, Projections.
1.2 Vectors, Inner Products, Lengths.
1.3 Subspaces, Projections.
1.5 Some History.
1.6 Projection Operators.
1.7 Eigenvalues and Eigenvectors.
2 Random Vectors.
2.1 Covariance Matrices.
2.2 Expected Values of Quadratic Forms.
2.3 Projections of Random Variables.
2.4 The Multivariate Normal Distribution.
2.5 The χ2, F, and t Distributions.
3 The Linear Model.
3.1 The Linear Hypothesis.
3.2 Confidence Intervals and Tests on η = c1ß1 + . . . + ckßk.
3.3 The Gauss-Markov Theorem.
3.4 The Gauss-Markov Theorem For The General Case.
3.5 Interpretation of Regression Coefficients.
3.6 The Multiple Correlation Coefficient.
3.7 The Partial Correlation Coefficient.
3.8 Testing H0 : θ ε V0 С V.
3.9 Further Decomposition of Subspaces.
3.10 Power of the F-Test.
3.11 Confidence and Prediction Intervals.
3.12 An Example from SAS.
3.13 Another Example: Salary Data.
4 Fitting of Regression Models.
4.1 Linearizing Transformations.
4.2 Specification Error.
4.3 Generalized Least Squares.
4.4 Effects of Additional or Fewer Observations.
4.5 Finding the "Best" Set of Regressors.
4.6 Examination of Residuals.
4.8 Asymptotic Normality.
4.9 Spline Functions.
4.10 Nonlinear Least Squares.
4.11 Robust Regression.
4.12 Bootstrapping in Regression.
4.13 Quantile Regression.
5 Simultaneous Confidence Intervals.
5.1 Bonferroni Confidence Intervals.
5.2 Scheffé Simultaneous Confidence Intervals.
5.3 Tukey Simultaneous Confidence Intervals.
5.4 Comparison of Lengths.
5.5 Bechhofer's Method.
6 Two-and Three-Way Analyses of Variance.
6.1 Two-Way Analysis of Variance.
6.2 Unequal Numbers of Observations Per Cell.
6.3 Two-Way Analysis of Variance, One Observation Per Cell.
6.4 Design of Experiments.
6.5 Three-Way Analysis of Variance.
6.6 The Analysis of Covariance.
7 Miscellaneous Other Models.
7.1 The Random Effects Model.
7.3 Split Plot Designs.
7.4 Mixed Models.
7.5 Balanced Incomplete Block Designs.
8 Analysis of Frequency Data.
8.2 Distribution Theory.
8.3 Conf. Ints. on Poisson and Binomial Parameters.
8.4 Log-Linear Models.
8.5 Estimation for the Log-Linear Model.
8.6 Chi-Square Goodness-of-Fit Statistics.
8.7 Limiting Distributions of the Estimators.
8.8 Logistic Regression.
The Statistical Language R.
A thorough discussion of mixed models, nonparametric regression, quantile regression, and Bayesian models.
All of the examples have been updated, and a greater emphasis is placed on computer-driven examples using S-Plus®, R, and SAS® code.
Figures illustrating the results of the computer-driven simulations have also been added.
This new edition emphasizes the geometry of vector spaces (the coordinate free approach) because the author has found that the intuition it provides is vital to the understanding of the theory.
Discussions on multiple comparison procedures, estimation of quantiles for regression models, and curve fitting of models have been added to the new edition.
The author clearly discusses and illustrates key concepts with interesting examples, and the presentation of the material is systematic and natural.
A list of problems that are suitable for homework exercises are at the end of each chapter, and selected solutions are available at the end of the book.