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 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.
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