Linear RegressionSpringer Science & Business Media, 25. 7. 2003. - 394 страница In linear regression the ordinary least squares estimator plays a central role and sometimes one may get the impression that it is the only reasonable and applicable estimator available. Nonetheless, there exists a variety of alterna tives, proving useful in specific situations. Purpose and Scope. This book aims at presenting a comprehensive survey of different point estimation methods in linear regression, along with the the oretical background on a advanced courses level. Besides its possible use as a companion for specific courses, it should be helpful for purposes of further reading, giving detailed explanations on many topics in this field. Numerical examples and graphics will aid to deepen the insight into the specifics of the presented methods. For the purpose of self-containment, the basic theory of linear regression models and least squares is presented. The fundamentals of decision theory and matrix algebra are also included. Some prior basic knowledge, however, appears to be necessary for easy reading and understanding. |
Садржај
Forschungsgemeinschaft DFG under grants Tr 25331 and Tr 25332 | 3 |
The Linear Regression Model | 33 |
6 | 69 |
3 | 89 |
5 | 150 |
Linear Admissibility | 213 |
ст | 259 |
3 | 266 |
6 | 289 |
A Matrix Algebra | 331 |
B Stochastic Vectors | 359 |
An Example Analysis with R | 369 |
References | 381 |
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Чести термини и фразе
admissible for ẞ B₁ coefficient of determination collinearity compute Consider the linear convex combination corresponding Cov(B covariance matrix decision rule denotes eigenvalues estimator for ẞ given holds true homogeneous linear estimator i-th identity independent variables inequality least squares estimator least squares variance linear Bayes estimator linear regression model linearly admissible estimators loss function main diagonal elements mator minimax model assumption model with assumptions MSE(B MSE(B,B non-stochastic nonnegative definite matrix observed unweighted squared obtain ordinary least squares orthogonal orthogonal matrix outliers parameter space point estimators principal components estimator Problem random vector residuals respect restricted least squares ridge estimator ridge trace satisfied Sect Show shrinkage estimator squared error loss squared error risk Statistics Stein estimator studentized residuals symmetric matrix symmetric nonnegative definite Theorem true parameter vector unbiased estimator uniformly better unweighted squared error values vector ẞ Xẞ
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