The Coordinate-Free Approach to Linear Models

This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with non-random predictors in a finite-dimensional setting. This approach is more insightful, more elegant, more direct, and simpler than the more common matrix approach to linear regression, analysis of variance, and analysis of covariance models in statistics. The book discusses the intuition behind and optimal properties of various methods of estimating and testing hypotheses about unknown parameters in the models. Topics covered range from linear algebra, such as inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and non-optimal properties of Gauss-Markov, Bayes, and shrinkage estimators under assumption of normality, the optimal properties of F-test, and the analysis of covariance and missing observations.

1. Introduction; 2. Topics in linear algebra; 3. Random vectors; 4. Gauss-Markov estimation; 5. Normal theory: estimation; 6. Normal theory: testing; 7. Analysis of covariance; 8. Missing observations.

The coordinate-free, or geometric, approach to the theory of linear models is more insightful, more elegant, more direct, and simpler than the more common matrix approach. This book treats Model I ANOVA and linear regression models with non-random predictors in a finite-dimensional setting.

Professor Wichura has 37 years of teaching experience in the Department of Statistics at the University of Chicago. He has served as an Associate Editor for the Annals of Probability and was the Database Editor for the Current Index to Statistics from 1995 to 2000. He is the author of the PiCTeX macros (for drawing pictures in TeX) and the PiCTeX manual, and also of the TABLE macros and the TABLE manual.