Ebook: Linear Models and Generalizations: Least Squares and Alternatives

Thebookisbasedonseveralyearsofexperienceofbothauthorsinteaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and o?ers a selectionofclassicalandmodernalgebraicresultsthatareusefulinresearch work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss fu- tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and a variety of practical applications will be useful not only to students but also to researchers and consultants in statistics.

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Thoroughly revised and updated with the latest results, this Third Edition provides an up-to-date account of the theory and applications of linear models. The authors present a unified theory of inference from linear models and its generalizations with minimal assumptions. They not only use least squares theory, but also alternative methods of estimation and testing based on convex loss functions and general estimating equations.

Some of the highlights you’ll discover in this text include sensitivity analysis and model selection, an analysis of incomplete data, and an analysis of categorical data based on a unified presentation of generalized linear models. You’ll also find an extensive appendix on matrix theory that is particularly useful for researchers in econometrics, engineering, and optimization theory.

This text is recommended for courses in statistics at the graduate level. It also serves as a supplemental text for other courses in which linear models play a role.

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Thoroughly revised and updated with the latest results, this Third Edition provides an up-to-date account of the theory and applications of linear models. The authors present a unified theory of inference from linear models and its generalizations with minimal assumptions. They not only use least squares theory, but also alternative methods of estimation and testing based on convex loss functions and general estimating equations.

Some of the highlights you’ll discover in this text include sensitivity analysis and model selection, an analysis of incomplete data, and an analysis of categorical data based on a unified presentation of generalized linear models. You’ll also find an extensive appendix on matrix theory that is particularly useful for researchers in econometrics, engineering, and optimization theory.

This text is recommended for courses in statistics at the graduate level. It also serves as a supplemental text for other courses in which linear models play a role.

Content:
Front Matter....Pages i-xix
Introduction....Pages 1-5
The Simple Linear Regression Model....Pages 7-31
The Multiple Linear Regression Model and Its Extensions....Pages 33-141
The Generalized Linear Regression Model....Pages 143-221
Exact and Stochastic Linear Restrictions....Pages 223-269
Prediction in the Generalized Regression Model....Pages 271-319
Sensitivity Analysis....Pages 321-356
Analysis of Incomplete Data Sets....Pages 357-392
Robust Regression....Pages 393-409
Models for Categorical Response Variables....Pages 411-487
Back Matter....Pages 489-572

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Thoroughly revised and updated with the latest results, this Third Edition provides an up-to-date account of the theory and applications of linear models. The authors present a unified theory of inference from linear models and its generalizations with minimal assumptions. They not only use least squares theory, but also alternative methods of estimation and testing based on convex loss functions and general estimating equations.

Some of the highlights you’ll discover in this text include sensitivity analysis and model selection, an analysis of incomplete data, and an analysis of categorical data based on a unified presentation of generalized linear models. You’ll also find an extensive appendix on matrix theory that is particularly useful for researchers in econometrics, engineering, and optimization theory.

This text is recommended for courses in statistics at the graduate level. It also serves as a supplemental text for other courses in which linear models play a role.

Content:
Front Matter....Pages i-xix
Introduction....Pages 1-5
The Simple Linear Regression Model....Pages 7-31
The Multiple Linear Regression Model and Its Extensions....Pages 33-141
The Generalized Linear Regression Model....Pages 143-221
Exact and Stochastic Linear Restrictions....Pages 223-269
Prediction in the Generalized Regression Model....Pages 271-319
Sensitivity Analysis....Pages 321-356
Analysis of Incomplete Data Sets....Pages 357-392
Robust Regression....Pages 393-409
Models for Categorical Response Variables....Pages 411-487
Back Matter....Pages 489-572
....