Coord-Free Approach Linear Models

English

Series: Cambridge Series in Statistical and Probabilistic Mathematics Ser.

ISBN: 0511346077

EAN: 9780511346071

Category: Mathematics / Probability & Statistics / Regression Analysis/Mathematics / Probability & Statistics / General/

Publisher: Cambridge University Press

Release Date: 10/31/2006

Synopsis: 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.

Excerpt: Unknown Property Excerpt

Coord-Free Approach Linear Models

Illustrated: No

Format: eBook - PDF

Pages: 216