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Regression estimators : a comparative study /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston :
Academic Press,
�1990.
|
| Colección: | Statistical modeling and decision science.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Regression Estimators: A Comparative Study; Copyright Page; Table of Contents; Preface; Part I: Introduction and Mathematical Preliminaries; Chapter I. Introduction; 1.0. Motivation for Writing This Book; 1.1. Purpose of This Book; 1.2. Least Square Estimators and the Need for Alternatives; 1.3. Historical Survey; 1.4. The Structure of the Book; Chapter II. Mathematical and Statistical Preliminaries; 2.0. Introduction; 2.1. Matrix Theory Results; 2.2. The Bayes Estimator; 2.3. The Minimax Estimator; 2.4. Criterion for Comparing Estimators: Theobald's1974 Result.
- 2.5. Some Useful Inequalities2.6. Some Miscellaneous Useful Matrix Results; 2.7. Summary; Part II: The Estimators; Chapter III. The Estimators; 3.0. Introduction; 3.1. The Least Square Estimator and Its Properties; 3.2. The Generalized Ridge Regression Estimator; 3.3. The Mixed Estimators; 3.4. The Linear Minimax Estimator; 3.5. The Bayes Estimator; 3.6. Summary and Remarks; Chapter IV. How the Different Estimators Are Related; 4.0. Introduction; 4.1. Alternative Forms of the Bayes Estimator Full Rank Case; 4.2. Alternative Forms of the Bayes Estimator Non-FullRank Case.
- 4.3. The Equivalence of the Generalized Ridge Estimatorand the Bayes Estimator4.4. The Equivalence of the Mixed Estimatorand the BayesEstimator; 4.5. Ridge Estimators in the Literature as Special Cases ofthe BE, Minimax Estimators, or Mixed Estimators; 4.6. Extension of Results to the Case where U'FU Is Not PositiveDefinite; 4.7. An Extension of the Gauss-Markov Theorem; 4.8. Summary and Remarks; Part III: The Efficiencies of the Estimators; Chapter V. Measures of Efficiency of the Estimators; Chapter VI. The Average MSE; 6.0. Introduction.
- 6.1. The Forms of the MSE for the Minimax, Bayes andthe Mixed Estimator6.2. Relationship Between the Average Variance and theMSE; 6.3. The Average Variance and the MSE of the BE; 6.4. Alternative Forms of the MSE of the Mixed Estimator; 6.5. Comparison of the MSE of Different BE; 6.6. Comparison of the Ridge and Contraction Estimator'sMSE; 6.7. Summary and Remarks; Chapter VII. The MSE Neglecting the Prior Assumptions; 7.0. Introduction; 7.1. The MSE of the BE; 7.2. The MSE of the Mixed Estimators Neglecting the Prior Assumptions.
- 7.3. The Comparison of the Conditional MSE of the Bayes Estimator and the Least Square Estimator and the Comparison of the Conditional and the AverageMSE7.4. The Comparison of the MSE of a Mixed Estimatorwith the LS Estimators; 7.5. The Comparison of the MSE of Two BE; 7.6. Summary; Chapter VIII. The MSE for Incorrect Prior Assumptions; 8.0. Introductio; 8.1. The BE and Its MSE; 8.2. The Minimax Estimator; 8.3. The Mixed Estimator; 8.4. Contaminated Priors; 8.5. Contaminated (Mixed) Bayes Estimators; 8.6. Summary; Part IV: Applications; Chapter IX. The Kaiman Filter; 9.0. Introduction; 9.1. The Kaiman Filter as a BayesEstimator.