Ebook: Linear Models: Least Squares and Alternatives

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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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.
Content:
Front Matter....Pages i-xv
Introduction....Pages 1-3
Linear Models....Pages 5-21
The Linear Regression Model....Pages 23-96
The Generalized Linear Regression Model....Pages 97-136
Exact and Stochastic Linear Restrictions....Pages 137-180
Prediction Problems in the Generalized Regression Model....Pages 181-210
Sensitivity Analysis....Pages 211-240
Analysis of Incomplete Data Sets....Pages 241-270
Robust Regression....Pages 271-287
Models for Categorical Response Variables....Pages 289-352
Back Matter....Pages 353-428

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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.
Content:
Front Matter....Pages i-xv
Introduction....Pages 1-3
Linear Models....Pages 5-21
The Linear Regression Model....Pages 23-96
The Generalized Linear Regression Model....Pages 97-136
Exact and Stochastic Linear Restrictions....Pages 137-180
Prediction Problems in the Generalized Regression Model....Pages 181-210
Sensitivity Analysis....Pages 211-240
Analysis of Incomplete Data Sets....Pages 241-270
Robust Regression....Pages 271-287
Models for Categorical Response Variables....Pages 289-352
Back Matter....Pages 353-428
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