Linear Models and Generalizations: Least Squares and Alternatives 2nd Edition Pdf well written by C.R. Rao, Helge Toutenburg, Andreas Fieger, Christian Heumann, Thomas Nittner, Sandro Scheid. The book is based on several years of experience of both authors in teaching 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.The first edition of this book has found wide interest in the readership. A first reprint appeared in 1997 and a special reprint for the Peoples Republic of China appeared in 1998. Based on this, the authors followed the invitation of John Kimmel of Springer-Verlag to prepare a second edition, which includes additional material such as simultaneous confidence intervals for linear functions, neural networks, restricted regression and selection problems (Chapter 3); mixed effect models, regression-like equations in econometrics, simultaneous prediction of actual and average values, simultaneous estimation of parameters in different linear models by empirical Bayes solutions (Chapter 4); the method of the Kalman Filter (Chapter 6);and regression diagnostics for removing an observation with animating graphics (Chapter 7).
A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results about the definiteness of matrices, especially for the differences of matrices, which enable superiority comparisons of two biased estimates to be made for the first time. We have attempted to provide a unified 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 functions 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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