Robust statistics for signal processing /
| Main Authors: | , , , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY, USA :
Cambridge University Press,
2018.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Half-title; Title page; Copyright information; Contents; Preface; Abbreviations; List of Symbols; 1 Introduction and Foundations; 1.1 History of Robust Statistics; 1.2 Robust M-estimators for Single-Channel Data; 1.2.1 Location and Scale Estimation; Maximum Likelihood Estimation of Location and Scale; M-estimation of Location and Scale; 1.3 Measures of Robustness; 1.3.1 The Influence Function and Qualitative Robustness; Sensitivity Curve; The Influence Function; Qualitative Robustness of an Estimator; 1.3.2 The Breakdown Point and Quantitative Robustness; The Breakdown Point
- The Maximum-Bias Curve1.4 Concluding Remarks; 2 Robust Estimation: The Linear Regression Model; 2.1 Complex Derivatives and Optimization; 2.2 The Linear Model and Organization of the Chapter; 2.3 The Least Squares Estimator; 2.4 Least Absolute Deviation and Rank-Least Absolute Deviation Regression; 2.4.1 Simple Linear Regression without an Intercept; Weighted Median Regression: The Real-Valued Case; Weighted Median Regression: The Complex-Valued Case; 2.4.2 Simple Linear Regression with Intercept; 2.4.3 Computation of Least Absolute Deviation and Rank-Least Absolute Deviation Estimates
- 2.5 ML- and M-estimates of Regression with an Auxiliary Scale Estimate2.5.1 Objective Function Approach vs. Estimating Equation Approach; 2.5.2 Examples of Loss Functions; 2.5.3 Computation Using the Iteratively Reweighted Least Squares Algorithm; 2.6 Joint M-estimation of Regression and Scale Using Huber's Criterion; 2.6.1 Minimization-Majorization Algorithm; 2.6.2 Minimization-Majorization Algorithm for Huber's Criterion; 2.7 Measures of Robustness; 2.7.1 Outliers in the Linear Regression Model; 2.7.2 (p+1)-dimensional Influence Function; 2.7.3 Breakdown Point
- 3.3.2 Subgradient Equations for the Lasso/Elastic Net3.3.3 Computation of the Lasso/Elastic Net; Cyclic Coordinate Descent Algorithm; Pathwise Coordinate Descent; 3.4 The Least Absolute Deviation-Lasso and the Rank-Lasso; 3.4.1 Simple Linear Regression (p = 1); 3.4.2 The Computation of Least Absolute Deviation-Lasso and Rank-Lasso Estimates: p > 1 Case; 3.4.3 The Fused Rank-Lasso; Image Denoising Example; 3.5 Joint Penalized M-estimation of Regression and Scale; 3.5.1 Algorithm; 3.6 Penalty Parameter Selection; 3.7 Application Example: Prostate Cancer; 3.8 Concluding Remarks