Publisher: John Wiley (2008)Details: 241 pages, Hardcover
Series: Wiley Series in Probability and Statistics
Price: $90.00
ISBN: 9780470025666
Category: Textbook
Topics: Analysis of Variance, Linear Models, Statistics
Brenton R. Clarke
Publisher: John Wiley (2008)
Details: 241 pages, Hardcover
Series: Wiley Series in Probability and Statistics
Price: $90.00
ISBN: 9780470025666
Category: Textbook
Topics: Analysis of Variance, Linear Models, Statistics
[Reviewed by Ita Cirovic Donev, on 01/13/2009]
Linear Models is yet another reference in the field. What would be the proper role for it? There are many books out there that discuss linear models and ANOVA, some good, some not so good. The authors always claim that theirs is something different and, of course, better than the competition. This book does present a different approach. From author’s words:
Where this book differs significantly from most books on ANOVA is in the [discussion] beginning with Helmer matrices and Kronecker products… which allows succinct and explicit forms of contrast that yield both the orthogonal components in ANOVA, including projection matrices, and distributions of component sums of squares with illustrations for a number of designs, including two-way ANOVA, Latin squares, and 2k factorial designs.
So let’s see how well it works.
The author takes some time to introduce the subject, providing a nice first chapter on fixed effects and presenting some common linear models. The next three chapters also, in my opinion, constitute the introduction or preparation to the subject. Hence, we can refresh our mind with some vector space theory and in particular a discussion of orthogonal projections onto subspaces. This then directly leads us to least square theory and the Gauss-Markov theorem. The author does not delve much into discussion but rather presents the important results. To finalize the introduction, some distribution theory is presented.
Given the required prerequisite knowledge of matrix theory, mathematical statistics and probability theory, these four chapters should be easily grasped. Theorems are stated with full proofs, there is no hand-waving. Even some more trivial steps are shown.
Chapter 5 presents orthogonal relationships, including theoretical results for Helmert matrices and Kronecker product. The presentation is detailed and transparent enough to be easily followed and understandable. Some simpler examples are provided, and one more detailed example showing the calculation steps along the way. This easy to follow chapter provides a sound base for the rest of the book. The rest of the book deals with the methods of estimation and fitting as well as discussing robust methods.
The book is pitched at the graduate level, so it is written assuming quite a wide base knowledge of statistics, probability and matrix theory. Proofs are detailed without skipping too many steps. Exercises are provided and accompany the text quite nicely. Overall, it is hard for me to imagine this book as a main text for the course, but as a side reference it should be more than welcomed.
Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.