David A. Harville: Linear models and the relevant distributions and matrix algebra
Sometimes you read a book, and you think: ‘Why didn’t someone write this before now?’ This is one of those books.
The linear model is one of the key “work horse” models in statistics, and it provides a stepping-stone to many other important models and associated statistical techniques. A thorough understanding of the statistical and algebraic (and/or geometrical) foundations of this model is a core requirement for anyone training or researching in statistical modeling.
To be sure, there are many excellent books that provide either introductory or advanced discussions of the linear model. However, one of Harville’s major contributions is that this monograph covers both the requisite linear algebra and the statistical theory in a very thorough and balanced manner. It provides a one-stop source of boththe statistical and algebraic information needed for a deep understanding of the linear statistical model. In addition, of course, the large range of “tools” that are introduced and...