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Linear Model Theory Univariate, Multivariate, and Mixed Models

Автор: Bo0mB0om » 21 ноября 2015
Linear Model Theory Univariate, Multivariate, and Mixed Models

Linear Model Theory: Univariate, Multivariate, and Mixed Models
by Keith E. Muller, Paul W. Stewart
English | 2006 | ISBN: 0471214884 | 410 pages | PDF | 35.24 MB

"A precise and accessible presentation of linear model theory, illustrated with data examples Statisticians often use linear models for data analysis and for developing new statistical methods. Most books on the subject have historically discussed univariate, multivariate, and mixed linear models separately, whereas presents a unified treatment in order to make clear the distinctions among the three classes of models. begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation. Data examples motivate and illustrate the models. Chapters 7-10 address distribution theory of multivariate Gaussian variables and quadratic forms. Chapters 11-19 detail methods for estimation, hypothesis testing, and confidence intervals. The final chapters, 20-23, concentrate on choosing a sample size. Substantial sets of excercises of varying difficulty serve instructors for their classes, as well as help students to test their own knowledge. The reader needs a basic knowledge of statistics, probability, and inference, as well as a solid background in matrix theory and applied univariate linear models from a matrix perspective. Topics covered include:
* A review of matrix algebra for linear models
* The general linear univariate model
* The general linear multivariate model
* Generalizations of the multivariate linear model
* The linear mixed model
* Multivariate distribution theory
* Estimation in linear models
* Tests in Gaussian linear models
* Choosing a sample size in Gaussian linear models Filling the need for a text that provides the necessary theoretical foundations for applying a wide range of methods in real situations, centers on linear models of interval scale responses with finite second moments. Models with complex predictors, complex responses, or both, motivate the presentation."

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