Linear Model Theory (eBook)

Univariate, Multivariate, and Mixed Models

Keith E. Muller, Paul W. Stewart (Autoren)

eBook Download: PDF

2006 | 1. Auflage
424 Seiten
John Wiley & Sons (Verlag)
9780470052136 (ISBN)

Infos

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 Linear Model Theory: Univariate,
Multivariate, and Mixed Models presents a unified treatment in
order to make clear the distinctions among the three classes of
models.

Linear Model Theory: Univariate, Multivariate, and Mixed
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, Linear Model Theory: Univariate, Multivariate,
and Mixed Models centers on linear models of interval scale
responses with finite second moments. Models with complex
predictors, complex responses, or both, motivate the
presentation.

Autor

KEITH E. MULLER, PhD, is Professor and Director of the Division of Biostatistics in the Department of Epidemiology and Health Policy Research in the College of Medicine at the University of Florida in Gainesville, as well as Professor Emeritus of Biostatistics at The University of North Carolina at Chapel Hill where the book was written. PAUL W. STEWART, PhD, is Research Associate Professor of Biostatistics at The University of North Carolina at Chapel Hill.

Rezensionen

"This text successfully offers a unified context for the theory of
univariate, multivariate, and mixed modeling settings and may be
useful supplemental text for individuals interested in multivariate
modeling." (Journal of the American Statistician, December
2008)

"I believe that this text provides an important contribution to
the long-memory time series literature. I feel that it
largely achieves its aims and could be useful for those instructors
wishing to teach a semester-long special topics course ... .I
strongly recommend this book to anyone interested in long-memory
time series. Both researchers and beginners alike will find
this text extremely useful." (Journal of the American
Statistician, December 2008)

"The book will certainly be useful for Ph.D. students and
researchers in biostatistics who want to learn a little bit of
theory of linear models." (Mathematical Reviews, 2007)

"...stands out from the others...will certainly have its
enthusiastic supporters." (Biometrics, March 2007)

"...an excellent book for graduate students and professional
researchers." (MAA Reviews, February 2007)

"The focus of this book is on linear models with correlated
observations and Gaussian errors." (Zentralblatt MATH, April
2007)

Produkt-Details

• Erscheint lt. Verlag: 6.10.2006
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Angew. Wahrscheinlichkeitsrechn. u. Statistik / Modelle • Applied Probability & Statistics - Models • Multivariate Analyse • multivariate analysis • Statistics • Statistik
• ISBN-13: 9780470052136 / 9780470052136