Linear Models and Generalizations: Least Squares and AlternativesSpringer Science & Business Media, 15 de out. de 2007 - 572 páginas 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. |
Conteúdo
1 | |
4 | |
The Multiple Linear Regression Model and Its Extensions | 33 |
21 | 39 |
Sensitivity Analysis | 69 |
Classification and Regression Trees CART | 117 |
Projection Pursuit Regression | 124 |
Neural Networks and Nonparametric Regression Logistic Regression and Neural Networks Functional Data Analysis FDA Restricted Regression 3 28 ... | 130 |
98 | 290 |
4 | 292 |
7 | 298 |
Analysis of Incomplete Data Sets | 304 |
Simultaneous Prediction of Actual and Average Values of | 306 |
178 | 308 |
7 | 321 |
9 | 364 |
Complements | 138 |
11 | 145 |
1 | 157 |
The Aitken Estimator Misspecification of the Dispersion Matrix Heteroscedasticity and Autoregression | 167 |
2 | 190 |
Exercises | 220 |
Maximum Likelihood Estimation under Exact Restrictions | 227 |
49 | 231 |
Stepwise Inclusion of Exact Linear Restrictions Biased Linear Restrictions and MDE Comparison with | 233 |
79 | 237 |
MDE Matrix Comparison of Two Linear Biased | 242 |
112 | 243 |
3 | 247 |
137 | 249 |
SteinRule Estimators under Exact Restrictions | 251 |
174 | 257 |
Prediction in the Generalized Regression Model | 270 |
Prediction Regions | 287 |
Robust Regression | 393 |
Models for Categorical Response Variables | 410 |
199 | 455 |
215 | 462 |
233 | 468 |
243 | 478 |
269 | 485 |
ix | 493 |
Software for Linear Regression Models | 531 |
538 | |
546 | |
555 | |
557 | |
563 | |
564 | |
565 | |
570 | |
Outras edições - Ver todos
Linear Models and Generalizations Calyampudi R. Rao,Helge Toutenburg,Shalabh Prévia não disponível - 2008 |
Linear Models and Generalizations: Least Squares and Alternatives C. Radhakrishna Rao,Helge Toutenburg,Shalabh,Christian Heumann Prévia não disponível - 2010 |
Termos e frases comuns
ˆβ according additional alternative analysis apply assume assumptions asymptotic called choice classical coefficient column compared components condition consider consistent constant correlation corresponding covariance matrix criterion defined definite denote dependent derived determination difference discussed dispersion distribution effects equations equivalent error example Exercise exists expected explanatory variables expression function Further given gives Hence holds hypotheses identical independent individuals interest interval known leads likelihood linear model maximum mean measurement method minimizing missing mixed normal Note observations obtain OLSE optimal parameters positive prediction predictor probability problem procedure properties random rank reduced regression model relation relationship residuals respectively response restrictions risk sample selection solution statistic stochastic structure Suppose term Theorem true unbiased estimator unknown values variables variance vector weight zero
Passagens mais conhecidas
Página vi - Preface to the Second Edition The first edition of this book has enjoyed a gratifying existence.