The Coordinate-Free Approach to Linear Models

ISBN-13: 9780521868426 / Angielski / Twarda / 2006 / 214 str.

Michael J. Wichura

Opis

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 nonrandom 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 include inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and nonoptimal properties of Gauss-Markov, Bayes, and shrinkage estimators under the assumption of normality, the optimal properties of F-tests, and the analysis of covariance and missing observations.

Recenzje

'Compelementary subjects are sketched in sequences of insightful exercises to the reader.' Zentralblatt MATH

Spis treści

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.