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The coordinate-free approach to linear models /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The coordinate-free approach to linear models // Michael J. Wichura.
Author:	Wichura, Michael J.
Description:	1 online resource (xiii, 199 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Linear models (Statistics) -
Online resource:	https://doi.org/10.1017/CBO9780511546822
ISBN:	9780511546822 (ebook)

The coordinate-free approach to linear models /
Wichura, Michael J.

The coordinate-free approach to linear models /Michael J. Wichura. - 1 online resource (xiii, 199 pages) :digital, PDF file(s). - Cambridge series on statistical and probabilistic mathematics ;19. - Cambridge series on statistical and probabilistic mathematics ;32..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Topics in linear algebra -- Random vectors -- Gauss-Markov estimation -- Normal theory: estimation -- Normal theory: testing -- Analysis of covariance -- Missing observations.

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.

ISBN: 9780511546822 (ebook)Subjects--Topical Terms:

632956
Linear models (Statistics)

LC Class. No.: QA279 / .W53 2006

Dewey Class. No.: 519.5

The coordinate-free approach to linear models /
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505 0 $a Topics in linear algebra -- Random vectors -- Gauss-Markov estimation -- Normal theory: estimation -- Normal theory: testing -- Analysis of covariance -- Missing observations.
520 $a 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.
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650 0 $a Regression analysis. $3 569541
650 0 $a Analysis of covariance. $3 889898
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830 0 $a Cambridge series on statistical and probabilistic mathematics ; $v 32. $3 1133567
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