Linear Models and Generalizations Least Squares and Alternatives / [electronic resource] :
by C. Radhakrishna Rao, Helge Toutenburg, Shalabh, Christian Heumann.
- 3rd ed. 2008.
- XIX, 572 p. online resource.
- Springer Series in Statistics, 0172-7397 .
- Springer Series in Statistics, .
The Simple Linear Regression Model -- The Multiple Linear Regression Model and Its Extensions -- The Generalized Linear Regression Model -- Exact and Stochastic Linear Restrictions -- Prediction in the Generalized Regression Model -- Sensitivity Analysis -- Analysis of Incomplete Data Sets -- Robust Regression -- Models for Categorical Response Variables.
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.
9783540742272
10.1007/978-3-540-74227-2 doi
Probabilities. Statistics . Economic theory. Mathematical statistics. Operations research. Decision making. Probability Theory and Stochastic Processes. Statistical Theory and Methods. Economic Theory/Quantitative Economics/Mathematical Methods. Probability and Statistics in Computer Science. Operations Research/Decision Theory.