Linear Models

The book is based on both authors' several years of experience 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. 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 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 its practical applica­ tions will be useful not only to students but also to researchers and con­ sultants in statistics.

Inhalt
1 Introduction.- 2 Linear Models.- 3 The Linear Regression Model.- 4 The Generalized Linear Regression Model.- 5 Exact and Stochastic Linear Restrictions.- 6 Prediction Problems in the Generalized Regression Model.- 7 Sensitivity Analysis.- 8 Analysis of Incomplete Data Sets.- 9 Robust Regression.- 10 Models for Binary Response Variables.- A Matrix Algebra.- A.1 Introduction.- A.2 Trace of a Matrix.- A.3 Determinant of a Matrix.- A.4 Inverse of a Matrix.- A.5 Orthogonal Matrices.- A.6 Rank of a Matrix.- A.7 Range and Null Space.- A.8 Eigenvalues and Eigenvectors.- A.9 Decomposition of Matrices.- A.10 Definite Matrices and Quadratic Forms.- A.11 Idempotent Matrices.- A.12 Generalized Inverse.- A.13 Projectors.- A.14 Functions of Normally Distributed Variables.- A.15 Differentiation of Scalar Functions of Matrices.- A.16 Miscellaneous Results, Stochastic Convergence.- B Tables.- References.

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