Linear Models and the Relevant Distributions and Matrix Algebra
Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It can be a valuable reference, a primary or secondary text in a graduate-level course on linear models, or a resource used (in a course on mathematical statistics) to illustrate various theoretical concepts in the context of a relatively complex setting of great practical importance.
- Provides coverage of matrix algebra that is extensive and relatively self-contained and does so in a meaningful context
- Provides thorough coverage of the relevant statistical distributions, including spherically and elliptically symmetric distributions
- Includes extensive coverage of multiple-comparison procedures (and of simultaneous confidence intervals), including procedures for controlling the k-FWER and the FDR
- Provides thorough coverage (complete with detailed and highly accessible proofs) of results on the properties of various linear-model procedures, including those of least squares estimators and those of the F test.
- Features the use of real data sets for illustrative purposes
- Includes many exercises
David Harville served for 10 years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories at Wright-Patterson AFB, Ohio, 20 years as a full professor in Iowa State University’s Department of Statistics where he now has emeritus status, and seven years as a research staff member of the Mathematical Sciences Department of IBM’s T.J. Watson Research Center. He has considerable relevant experience, having taught M.S. and Ph.D. level courses in linear models, been the thesis advisor of 10 Ph.D. graduates, and authored or co-authored two books and more than 80 research articles. His work has been recognized through his election as a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics and as a member of the International Statistical Institute.
Introduction. Matrix Algebra: a Primer. Random Vectors and Matrices. The General Linear Model. Estimation and Prediction: Classical Approach. Some Relevant Distributions and Their Properties. Confidence Intervals (or Sets) and Tests of Hypotheses.
"The book presents procedures for making statistical inferences on the basis of the classical linear statistical model, and discusses the various properties of those procedures. Supporting material on matrix algebra and statistical distributions is interspersed with a discussion of relevant inferential procedures and their properties. The coverage ranges from MS-level to advanced researcher. In particular, the material in chapters 6-7 is not covered in an approachable manner in any other books, and greatly generalizes the traditional normal-based linear regression model to the elliptical distributions, thus greatly elucidating the advanced reader on just how far this class of models can be extended. Refreshingly, the material also goes beyond the classical 20th century coverage to include some 21st century topics like microarray (big) data analysis, and control of false discovery rates in large scale experiments…From the point of view of an advanced instructor and researcher on the subject, I very strongly recommend publication…Note that…this book provides the coverage of 3 books, hence the title purporting to provide a ‘unified approach’ (of 3 related subjects) is indeed accurate."
~Alex Trindade, Texas Tech University
"The book is very well written, with exceptional attention to details. It provides detailed derivations or proofs of almost all the results, and offers in-depth coverage of the topics discussed. Some of these materials (e.g., spherical/elliptical distributions) are hard to find from other sources. Anyone who is interested in linear models should benefit from reading this book and find it especially useful for a thorough understanding of the linear-model theory in a unified framework... The book is a delight to read."
~Huaiqing Wu, Iowa State University
"This book is useful in two ways: an excellent text book for a graduate level linear models course, and for those who want to learn linear mod