Matrix Algebra for Linear Models - Hardcover

Gruber, Marvin H. J.

Hardcover

ISBN 10: 1118592557 ISBN 13: 9781118592557

Publisher: Wiley, 2013

Synopsis

A self-contained introduction to matrix analysis theory and applications in the field of statistics

Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data.

Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features:

• Methods of deriving results from the properties of eigenvalues and the singular value decomposition
• Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models
• A section on the generalized singular value decomposition
• Multiple chapter exercises with selected answers to enhance understanding of the presented material

Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.

About this title

About the Author:

MARVIN H. J. GRUBER, PHD, is Professor Emeritus in the School of Mathematical Sciences at Rochester Institute of Technology. He has authored several books and journal articles in his areas of research interest, which include improving the efficiency of regression estimators. Dr. Gruber is a member of the American Mathematical Society and the American Statistical Association.

Review:

“This book seems suitable for an advanced undergraduate and/or introductory master's level course . . . Four appealing features of this book are its inclusion of an overview, a summary, exercises (with answers provided), and numerical examples for all sections.”  (American Mathematical Society, 1 November 2015)

“The book is suitable for graduate and postgraduate students and researchers. This book is highly recommended.”  (Zentralblatt, 1 April 2015)

“This is an excellent and comprehensive presentation of the use of matrices for linear models. The writing is very clear, and the layout is excellent. It would serve well either as a class text or as the foundation for individual personal study.”  (International Statistical Review, 18 March 2014)

About this edition

• Publisher: Wiley
• Publication date: 2013
• ISBN 10: 1118592557
• ISBN 13: 9781118592557
• Binding: Hardcover
• Edition number: 1
• Number of pages: 392