Adaptive regression
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書誌事項
Adaptive regression
Springer, c2000
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注記
Bibliography: p. [159]-171
Includes indexes
内容説明・目次
内容説明
While there have been a large number of estimation methods proposed and developed for linear regression, none has proved good for all purposes. This text focuses on the construction of an adaptive combination of two estimation methods so as to help users make an objective choice and combine the desirable properties of two estimators.
目次
1 Prologue.- 1.1 Introduction.- 1.2 Adaptive Combination of Estimators.- 1.3 Notes.- 2 Regression Methods.- 2.1 Introduction.- 2.2 LS Regression.- 2.3 Ridge Regression.- 2.4 LAD Regression.- 2.5 M-Regression.- 2.6 L-Regression.- 2.7 Other Regression Estimators.- 2.8 Estimators of Scale Parameter.- 2.9 Notes.- 3 Adaptive LAD + LS Regression.- 3.1 Introduction.- 3.2 Convex Combination of LAD and LS Regressions.- 3.3 Adaptive Combination of LAD and LS Regressions.- 3.4 Illustrative Examples.- 3.5 Notes.- 4 Adaptive LAD + TLS Regression.- 4.1 Introduction.- 4.2 Adaptive Combination of LAD and Trimmed LS.- 4.3 An Example of Multiple Regression.- 4.4 Notes.- 5 Adaptive LAD + M-Regression.- 5.1 Introduction.- 5.2 Combination of LAD and M-Estimators.- 5.3 Adaptive Combination of LAD and M-Estimators.- 5.4 An Example of Multiple Regression.- 5.5 Notes.- 6 Adaptive LS + TLS Regression.- 6.1 Introduction.- 6.2 Adaptive Combination of Mean and Trimmed Mean.- 6.3 Adaptive Combination of LS and TLS Regressions.- 6.4 Example of Multiple Regression.- 6.5 Notes.- 7 Adaptive Choice of Trimming.- 7.1 Introduction.- 7.2 Fully Adaptive Trimmed Mean and TLS.- 7.3 Adaptive Choice for fhe Trimmed Mean.- 7.4 Adaptive Choice in Linear Model Based on Ranks.- 7.5 Adaptive Choice in Linear Model Based on Regression Rank Scores.- 7.6 Notes.- 8 Adaptive Combination of Tests.- 8.1 Introduction.- 8.2 Types of Tests.- 8.3 Adaptive Combination of F-Test and Median-Type Test.- 8.4 Adaptive Combination of M-Test and Median-Type Test.- 8.4.1 Continuation of the Example of Section 3.4.- 8.5 Notes.- 9 Computational Aspects.- 9.1 Introduction.- 9.2 Computing the Adaptive Combination of LS and LAD.- 9.2.1 Direct Procedure.- 9.2.2 Reweighted Least Squares.- 9.3 Program ADAPTIVE.- 10 Some Asymptotic Results.- 10.1 Asymptotic Properties of Studentized M-Estimators.- 10.2 Uniform Asymptotic Linearity of M-Statistics.- 10.3 Estimators of Scale Parameter.- 10.4 Optimal Choice of ?n.- 11 Epilogue.- References.- Author Index.
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