Abdelhak M. Zoubir, Technische Universität, Darmstadt, Germany, Visa Koivunen, Aalto University, Finland, Esa Ollila Aalto University, Finland, Michael Muma Technische Universität, Darmstadt, Germany.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New York, NY, USA :
Name of Publisher, Distributor, etc.
Cambridge University Press,
Date of Publication, Distribution, etc.
2018.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
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Includes bibliographical references and index.
CONTENTS NOTE
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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
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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
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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
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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
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SUMMARY OR ABSTRACT
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Understand the benefits of robust statistics for signal processing using this unique and authoritative text.