Linear Model Theory

Beschreibung

A precise and accessible presentation of linear model theory,illustrated with data examples Statisticians often use linear models for data analysis and fordeveloping new statistical methods. Most books on the subject havehistorically discussed univariate, multivariate, and mixed linearmodels separately, whereas Linear Model Theory: Univariate,Multivariate, and Mixed Models presents a unified treatment inorder to make clear the distinctions among the three classes ofmodels. Linear Model Theory: Univariate, Multivariate, and MixedModels begins with six chapters devoted to providing brief andclear mathematical statements of models, procedures, and notation.Data examples motivate and illustrate the models. Chapters 7-10address distribution theory of multivariate Gaussian variables andquadratic 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 ofexcercises of varying difficulty serve instructors for theirclasses, 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 andapplied univariate linear models from a matrix perspective. Topicscovered 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 necessarytheoretical foundations for applying a wide range of methods inreal situations, Linear Model Theory: Univariate, Multivariate,and Mixed Models centers on linear models of interval scaleresponses with finite second moments. Models with complexpredictors, complex responses, or both, motivate thepresentation.

Autor*in

Keith E. Muller

Themen in »Linear Model Theory«

Angew. Wahrscheinlichkeitsrechn. u. Statistik / Modelle Applied Probability & Statistics - Models Multivariate Analyse Multivariate Analysis Statistics Statistik

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"This text successfully offers a unified context for the theory ofunivariate, multivariate, and mixed modeling settings and may beuseful supplemental text for individuals interested in multivariatemodeling." (Journal of the American Statistician, December2008) "I believe that this text provides an important contribution tothe long-memory time series literature. I feel that itlargely achieves its aims and could be useful for those instructorswishing to teach a semester-long special topics course ... .Istrongly recommend this book to anyone interested in long-memorytime series. Both researchers and beginners alike will findthis text extremely useful." (Journal of the AmericanStatistician, December 2008) "The book will certainly be useful for Ph.D. students andresearchers in biostatistics who want to learn a little bit oftheory of linear models." (Mathematical Reviews, 2007) "...stands out from the others...will certainly have itsenthusiastic supporters." (Biometrics, March 2007) "...an excellent book for graduate students and professionalresearchers." (MAA Reviews, February 2007) "The focus of this book is on linear models with correlatedobservations and Gaussian errors." (Zentralblatt MATH, April2007)
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