The Coordinate-Free Approach to Linear Models
By addebook • Oct 14th, 2008 • Category: Mathematics
The Coordinate-Free Approach to Linear Models (Cambridge Series in Statistical and Probabilistic Mathematics)
The Coordinate-Free Approach to Linear Models (Cambridge Series in Statistical and Probabilistic Mathematics)
By Michael J. Wichura
Publisher: Cambridge University Press
Number Of Pages: 216
Publication Date: 2006-10-23
ISBN-10 / ASIN: 0521868424
ISBN-13 / EAN: 9780521868426
Binding: Hardcover
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.
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