(Springer Series in Statistics) C.Radhakrishna Rao, Helge Toutenburg, Christian Heumann, Thomas Nittner, Sandro Scheid-Linear Models_ Least Squares and Alternatives-Springer (1997).pdf

Linear Models: Least
Squares and Alternatives,
Second Edition
C. Radhakrishna Rao
Helge Toutenburg
Springer
Preface to the First Edition
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 panying 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 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 parisons 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 func-
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.
We would like to thank our colleagues Dr. G. Trenkler and Dr. V. K. Sri-
vastava for their valuable advice during the preparation of the book. We
vi Preface to the First Edition
wish to acknowledge our appreciation of the generous help received from
Andrea Sch¨opp, Andreas Fieger,