Linear Models: Least Squares and Alternatives (Springer Series in Statistics) Review

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(More customer reviews)I recently got a copy of this book (first edition). While I try to look up some result I need at hand (obviously I find it, the most general and accurate answer, a typical use of Rao's book such as his other classic linear inference book), I find myself digging deeper and deeper into other places of the book. While linear model books and courses are typically boring and contain little new, I find all the new and deep results everywhere in this book, and it's a joy and refreshing experience. For example, the discussion of generalized linear model in the context of heteroscedastic linear model is very natural. The chapter on linear and stochastic constraints is a must read for anybody deals with high-dimensional and complex data. The prediction theory is very novel and general. After closing this book, I'm thinking what more can be said about linear models. Obviously they are useful, not obsolete or unrealistic as being often misconceived. The morale is use in proper context and wariness against violations of model assumptions. There are plenty of tests and remedies in this book for the latter. A modern view is that many nonlinear methods can be treated as extensions of linear models such as nonparametric regression (linear smoothers and local polynomial method), neural networks, etc. and the second edition of this book has added substantial materials in this regard. In all, I recomend this book as an excellent textbook for a seond course on linear models, a must read for researchers dealing with some aspects of linear models, and a must-have reference for anyone who needs to check up the most complete and updated results on linear models.

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This book provides an up-to-date account of the theory and applications of linear models. It can be used as a text for courses in statistics at the graduate level as well as an accompanying text for other courses in which linear models play a part. The authors present a unified theory of inference from linear models with minimal assumptions, not only through least squares theory, but also using alternative methods of estimation and testing based on convex loss functions and general estimating equations. Some of the highlights include: - a special emphasis on sensitivity analysis and model selection; - a chapter devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models; - a chapter devoted to incomplete data sets; - an extensive appendix on matrix theory, useful to researchers in econometrics, engineering, and optimization theory; - a chapter devoted to the analysis of categorical data based on a unified presentation of generalized linear models including GEE- methods for correlated response; - a chapter devoted to incomplete data sets including regression diagnostics to identify Non-MCAR-processes The material covered will be invaluable not only to graduate students, but also to research workers and consultants in statistics. Helge Toutenburg is Professor for Statistics at the University of Muenchen. He has written about 15 books on linear models, statistical methods in quality engineering, and the analysis of designed experiments. His main interest is in the application of statistics to the fields of medicine and engineering.

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