Screen LibraryRegression estimators : a comparative study /
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| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Published: |
Academic Press,
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| Publisher Address: | Boston : |
| Publication Dates: | 1990. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Statistical modeling and decision science
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| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9780123047526 |
| Carrier Form: | 1 online resource (xi, 347 pages). |
| Bibliography: | Includes bibliographical references (pages 327-334) and index. |
| ISBN: |
9781483260976 1483260976 |
| Index Number: | QA278 |
| CLC: | O211.67 |
| Contents: |
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. |