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Other titles in the Springer Texts in Statistics series:
Plane Answers to Complex Questions (Springer Texts in Statistics)by Ronald Christensen
Synopses & Reviews
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate- level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes discussion of identifiability and its relationship to estimability, different approaches to the theories of testing parametric hypotheses and analysis of covariance, additional discussion of the geometry of least squares estimation and testing, new discussion of models for experiments with factorial treatment structures, and a new appendix on possible causes for getting test statistics that are so small as to be suspicious. Ronald Christensen is a Professor of Statistics at the University of New Mexico. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics.
This wide-ranging introduction to the use of linear models for analyzing data provides a unified treatment that includes analysis of variance models and regression models. This new edition includes discussion of identifiability, approaches to the theories of testing parametric hypotheses and analysis of covariance, the geometry of least squares estimation and testing, and possible causes for getting test statistics that are so small as to be suspicious.
Table of Contents
Introduction * Estimation * Testing Hypotheses * One-Way ANOVA * Multiple Comparison Techniques * Regression Analysis * Multifactor Analysis of Variance * Experimental Design Models * Analysis of Covariance * Estimation and Testing in General Gauss-Markov Models * Split Plot Models * Mixed Models and Variance Components * Checking Assumptions, Residuals, and Influential Observations * Variable Selection and Collinearity
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