Preface |
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ix | |
Abbreviations |
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xvi | |
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xx | |
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1 Introduction and Foundations |
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1 | (27) |
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1.1 History of Robust Statistics |
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1 | (4) |
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1.2 Robust M-estimators for Single-Channel Data |
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5 | (9) |
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1.3 Measures of Robustness |
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14 | (13) |
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27 | (1) |
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2 Robust Estimation: The Linear Regression Model |
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28 | (46) |
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2.1 Complex Derivatives and Optimization |
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28 | (3) |
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2.2 The Linear Model and Organization of the Chapter |
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31 | (2) |
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2.3 The Least Squares Estimator |
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33 | (3) |
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2.4 Least Absolute Deviation and Rank-Least Absolute Deviation Regression |
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36 | (10) |
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2.5 ML- and A/-estimates of Regression with an Auxiliary Scale Estimate |
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46 | (7) |
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2.6 Joint M-estimation of Regression and Scale Using Huber's Criterion |
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53 | (8) |
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2.7 Measures of Robustness |
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61 | (3) |
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2.8 Positive Breakdown Point Regression Estimators |
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64 | (3) |
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67 | (5) |
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72 | (2) |
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3 Robust Penalized Regression in the Linear Model |
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74 | (26) |
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3.1 Sparse Regression and Outline of the Chapter |
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74 | (2) |
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3.2 Extensions of the Lasso Penalty |
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76 | (1) |
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3.3 The Lasso and the Elastic Net |
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77 | (8) |
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3.4 The Least Absolute Deviation-Lasso and the Rank-Lasso |
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85 | (6) |
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3.5 Joint Penalized A/-estimation of Regression and Scale |
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91 | (4) |
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3.6 Penalty Parameter Selection |
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95 | (1) |
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3.7 Application Example: Prostate Cancer |
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96 | (2) |
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98 | (2) |
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4 Robust Estimation of Location and Scatter (Covariance) Matrix |
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100 | (25) |
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4.1 Complex Vector Space Isomorphism and Complex Distributions |
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101 | (2) |
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4.2 Elliptically Symmetric Distributions |
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103 | (6) |
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4.3 ML- and Af-estimation of the Scatter Matrix |
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109 | (3) |
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4.4 Examples of M- and ML-estimators |
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112 | (5) |
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4.5 Regularized M-estimators of the Scatter Matrix |
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117 | (2) |
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4.6 Signal Detection Application |
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119 | (4) |
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123 | (2) |
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5 Robustness in Sensor Array Processing |
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125 | (22) |
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125 | (2) |
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5.2 Basic Array Signal Model |
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127 | (4) |
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5.3 Uncertainties in the Array Signal Model |
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131 | (4) |
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5.4 Statistically Robust Methods |
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135 | (7) |
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5.5 Array Processing Examples |
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142 | (4) |
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146 | (1) |
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6 Tensor Models and Robust Statistics |
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147 | (16) |
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147 | (1) |
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6.2 Tensor Notation and Basic Operations |
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148 | (5) |
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6.3 Tensor Decompositions |
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153 | (2) |
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6.4 Robust Tensor Decomposition |
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155 | (2) |
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6.5 Combining Robustness with Sparsity |
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157 | (3) |
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160 | (2) |
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162 | (1) |
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163 | (23) |
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7.1 Robust Wiener Filtering |
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163 | (3) |
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7.2 Nonparametric Nonlinear Robust Filters |
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166 | (4) |
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7.3 Robust Kalman Filtering |
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170 | (7) |
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7.4 Robust Extended Kalman Filtering |
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177 | (8) |
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185 | (1) |
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8 Robust Methods for Dependent Data |
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186 | (31) |
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8.1 Signal and Outlier Models |
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186 | (4) |
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8.2 Propagation of Outliers |
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190 | (6) |
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8.3 An Overview of Robust Autoregressive Moving-Average Parameter Estimators |
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196 | (5) |
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8.4 Robust Model Order Selection |
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201 | (3) |
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8.5 Measures of Robustness |
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204 | (7) |
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211 | (5) |
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216 | (1) |
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9 Robust Spectral Estimation |
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217 | (16) |
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9.1 Robust Nonparametric Spectral Estimation |
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217 | (7) |
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9.2 Autoregressive Moving-Average Model-Based Robust Parametric Spectral Estimation |
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224 | (2) |
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9.3 Simulation Example: Robust Spectral Estimation |
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226 | (1) |
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9.4 Robust Subspace-Based Frequency Estimation |
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227 | (5) |
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232 | (1) |
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10 Robust Bootstrap Methods |
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233 | (25) |
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233 | (2) |
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10.2 Existing Robust Bootstrap Methods |
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235 | (6) |
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10.3 Robust Bootstrap Confidence Interval Estimation in Linear Regression |
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241 | (4) |
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10.4 Robust and Scalable Bootstrap for Large-Scale Data |
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245 | (12) |
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257 | (1) |
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11 Real-Life Applications |
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258 | (14) |
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11.1 Localization of User Equipment in an Indoor Environment |
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258 | (2) |
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11.2 Blood Glucose Concentration in Photometric Handheld Devices |
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260 | (2) |
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11.3 European Tracer Experiment Source Estimation |
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262 | (4) |
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11.4 Robust Short-Term Load Forecasting |
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266 | (2) |
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11.5 Robust Data Cleaning for Photoplethysmography-Based Pulse-Rate Variability Analysis |
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268 | (4) |
Bibliography |
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272 | (16) |
Index |
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288 | |