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  3. The Coordinate-Free Approach to Linear Models
  • Cited by 21
Publisher:
Cambridge University Press
Online publication date:
November 2009
Print publication year:
2006
Online ISBN:
9780511546822
DOI:
https://doi.org/10.1017/CBO9780511546822
Subjects:
Economics, Econometrics and Mathematical Methods, General Statistics and Probability, Statistical Theory and Methods, Statistics and Probability
Series:
Cambridge Series in Statistical and Probabilistic Mathematics (19)
Information

Book description

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.

Reviews

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

Source: Zentralblatt MATH

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