Linear Models and Generalizations: Least Squares and AlternativesThebookisbasedonseveralyearsofexperienceofbothauthorsinteaching 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. |
Contents
| 1 | |
| 9 | |
The Multiple Linear Regression Model and Its Extensions | 33 |
The Generalized Linear Regression Model 143 | 142 |
The Multivariate Regression Model | 192 |
8 | 209 |
Exact and Stochastic Linear Restrictions | 223 |
Prediction in the Generalized Regression Model 271 | 270 |
Sensitivity Analysis | 321 |
Graphics | 343 |
Analysis of Incomplete Data Sets | 357 |
6 | 367 |
1 | 393 |
Models for Categorical Response Variables 411 | 410 |
Software for Linear Regression Models | 531 |
| 563 | |
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Linear Models and Generalizations Calyampudi R. Rao,Helge Toutenburg,Shalabh No preview available - 2008 |
Common terms and phrases
analysis assume assumptions asymptotic b₁ biased coefficient condition consider correlation covariance matrix criterion defined denote derived dispersion matrix eigenvalues equations equivalent error estimator of ẞ estimator ẞ explanatory variables g-inverse given GLSE Hence idempotent independent interval K-vector least squares estimator linear estimator linear model linear regression linear regression model linear restrictions loss function M-estimation MDEP method minimizing missing values nonnegative definite nonparametric regression nonstochastic normal distribution obtain OLSE optimal parameters plim positive definite prediction predictor problem quadratic R₁ random variable rank(X regressors residuals respectively risk function sample scalar solution stochastic Studentized residuals sum of squares T₁ test statistic Theorem Toutenburg unbiased estimator unknown variance vector X₁ Xẞ zero β₁ βο σ² Χβ
Popular passages
Page vi - Preface to the Second Edition The first edition of this book has enjoyed a gratifying existence.