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The Coordinate-Free Approach to Linear Models
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  • Cited by 11
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Thomas, Neal 2017. Understanding MCP-MOD dose finding as a method based on linear regression. Statistics in Medicine, Vol. 36, Issue. 27, p. 4401.

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    Coussens, Anna K. Naude, Celeste E. Goliath, Rene Chaplin, George Wilkinson, Robert J. and Jablonski, Nina G. 2015. High-dose vitamin D3reduces deficiency caused by low UVB exposure and limits HIV-1 replication in urban Southern Africans. Proceedings of the National Academy of Sciences, Vol. 112, Issue. 26, p. 8052.

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    Rogers, Alan J. 2013. Concentration Ellipsoids, Their Planes of Support, and the Linear Regression Model. Econometric Reviews, Vol. 32, Issue. 2, p. 220.

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    Withers, Christopher S. and Nadarajah, Saralees 2011. Asymptotically optimal shrinkage estimates for non-normal data. Journal of Statistical Computation and Simulation, Vol. 81, Issue. 12, p. 2021.

    Wenke Xu and Fuxiang Liu 2010. Recursive algorithm of Generalized Least Squares Estimator. p. 487.

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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.


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

Source: Zentralblatt MATH

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