A Primer on Linear Models

Employing non-full-rank design matrices throughout, this text provides a concise yet solid foundation for understanding basic linear models. It introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss-Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The text presents proofs and discussions from both algebraic and geometric viewpoints and includes exercises of varying levels of difficulty at the end of each chapter.

Zusatztext "? I found the book very helpful. ? the result is very nice! very readable! and in particular I like the idea of avoiding leaps in the development and proofs! or referring to other sources for the details of the proofs. This is a useful well-written instructive book."-International Statistical Review"This work provides a brief! and also complete! foundation for the theory of basic linear models . . . can be used for graduate courses on linear models." - Nicoleta Breaz! Zentralblatt Math". . . well written . . . would serve well as the textbook for an introductory course in linear models! or as references for researchers who would like to review the theory of linear models." - Justine Shults! Department of Biostatistics! University of Pennsylvania School of Medicine! Journal of Biopharmaceutical Statistics Informationen zum Autor John F. Monahan Klappentext A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods. With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss-Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers. This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models. Zusammenfassung Employing non-full-rank design matrices throughout, this book enables understanding of basic linear models. This book introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss-Markov model. Inhaltsverzeichnis Preface. Examples of the General Linear Model. The Linear Least Squares Problem. Estimability and Least Squares Estimators. Gauss-Markov Model. Distributional Theory. Statistical Inference. Further Topics in Testing. Variance Components and Mixed Models. The Multivariate Linear Model. Appendices. Bibliography....

" I found the book very helpful. the result is very nice, very readable, and in particular I like the idea of avoiding leaps in the development and proofs, or referring to other sources for the details of the proofs. This is a useful well-written instructive book."International Statistical Review "This work provides a brief, and also complete, foundation for the theory of basic linear models . . . can be used for graduate courses on linear models." Nicoleta Breaz, Zentralblatt Math ". . . well written . . . would serve well as the textbook for an introductory course in linear models, or as references for researchers who would like to review the theory of linear models." Justine Shults, Department of Biostatistics, University of Pennsylvania School of Medicine, Journal of Biopharmaceutical Statistics

Autorentext

John F. Monahan

Klappentext

A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods. With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss-Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers. This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

Zusammenfassung
Employing non-full-rank design matrices throughout, this book enables understanding of basic linear models. This book introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss-Markov model.

Inhalt
Preface. Examples of the General Linear Model. The Linear Least Squares Problem. Estimability and Least Squares Estimators. Gauss-Markov Model. Distributional Theory. Statistical Inference. Further Topics in Testing. Variance Components and Mixed Models. The Multivariate Linear Model. Appendices. Bibliography.