Linear Models and Generalizations

1. Front Matter

   Pages i-xix

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2. Introduction

   Pages 1-5

3. The Simple Linear Regression Model

   Pages 7-31

4. The Multiple Linear Regression Model and Its Extensions

   Pages 33-141

5. The Generalized Linear Regression Model

   Pages 143-221

6. Exact and Stochastic Linear Restrictions

   Pages 223-269

7. Prediction in the Generalized Regression Model

   Pages 271-319

8. Sensitivity Analysis

   Pages 321-356

9. Analysis of Incomplete Data Sets

   Pages 357-392

10. Robust Regression

    Pages 393-409

11. Models for Categorical Response Variables

    Pages 411-487

12. Back Matter

    Pages 489-572

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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.

• Fitting
• Generalized linear model
• Least Squares
• Likelihood
• Optimization Theory
• Regression
• best fit
• calculus
• econometrics
• linear regression
• optimization
• statistics

From the reviews of the third edition:

"The book contains a massive amount of useful results related to the world of linear models. … I find my life more comfortable when I have this book in my bookshelf while checking whether some results have appeared in the literature. … a natural source book for a student and researcher of linear models. … written with great care and, of course, with great skills under the leadership of Professor C. Radhakrishna Rao. This is a very useful book and the authors earn congratulations." (Simo Puntanen, International Statistical Review, Vol. 75 (3), 2007)

"The book gives an up-to-date and comprehensive account of the theory and applications of linear models along with a number of new results. Throughout its ten chapters as well as its appendices, it covers theoretical issues and practical applications that make it suitable and useful not only to students but also to researchers and consultants in statistics." (Vangelis Grigoroudis, Zentralblatt MATH, Vol. 1151, 2009)

"This book has two laudable strengths. First, the coverage of topics is vast and varied. Second, extensive material is included on many modern, cutting-edge directions. … The book would also function as an excellent reference for graduate students and researchers on classical and current developments in linear model theory." (Joseph Cavanaugh, Journal of the American Statistical Association, Vol. 104 (486), June, 2009)

• Department of Statistics, Pennsylvania State University, University Park, USA

  C. Radhakrishna Rao

• Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur, India

  Shalabh

• Institut für Statistik, Ludwig-Maximilians-Universität, München, Germany

  Helge Toutenburg, Christian Heumann

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