{"product_id":"robust-statistics-theory-and-methods-with-r-second-edition-9781119214687","title":"Robust Statistics  Theory and Methods with R","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eNote: sections marked with an asterisk can be skipped on first reading.\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003ePreface to the First Edition xxi\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Classical and robust approaches to statistics 1\u003c\/p\u003e \u003cp\u003e1.2 Mean and standard deviation 2\u003c\/p\u003e \u003cp\u003e1.3 The “three sigma edit” rule 6\u003c\/p\u003e \u003cp\u003e1.4 Linear regression 8\u003c\/p\u003e \u003cp\u003e1.4.1 Straight-line regression 8\u003c\/p\u003e \u003cp\u003e1.4.2 Multiple linear regression 9\u003c\/p\u003e \u003cp\u003e1.5 Correlation coefficients 12\u003c\/p\u003e \u003cp\u003e1.6 Other parametric models 13\u003c\/p\u003e \u003cp\u003e1.7 Problems 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Location and Scale 17\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The location model 17\u003c\/p\u003e \u003cp\u003e2.2 Formalizing departures from normality 19\u003c\/p\u003e \u003cp\u003e2.3 M-estimators of location 22\u003c\/p\u003e \u003cp\u003e2.3.1 Generalizing maximum likelihood 22\u003c\/p\u003e \u003cp\u003e2.3.2 The distribution of M-estimators 25\u003c\/p\u003e \u003cp\u003e2.3.3 An intuitive view of M-estimators 28\u003c\/p\u003e \u003cp\u003e2.3.4 Redescending M-estimators 29\u003c\/p\u003e \u003cp\u003e2.4 Trimmed and Winsorized means 31\u003c\/p\u003e \u003cp\u003e2.5 M-estimators of scale 33\u003c\/p\u003e \u003cp\u003e2.6 Dispersion estimators 35\u003c\/p\u003e \u003cp\u003e2.7 M-estimators of location with unknown dispersion 37\u003c\/p\u003e \u003cp\u003e2.7.1 Previous estimation of dispersion 38\u003c\/p\u003e \u003cp\u003e2.7.2 Simultaneous M-estimators of location and dispersion 38\u003c\/p\u003e \u003cp\u003e2.8 Numerical computing of M-estimators 40\u003c\/p\u003e \u003cp\u003e2.8.1 Location with previously-computed dispersion estimation 40\u003c\/p\u003e \u003cp\u003e2.8.2 Scale estimators 41\u003c\/p\u003e \u003cp\u003e2.8.3 Simultaneous estimation of location and dispersion 42\u003c\/p\u003e \u003cp\u003e2.9 Robust confidence intervals and tests 42\u003c\/p\u003e \u003cp\u003e2.9.1 Confidence intervals 42\u003c\/p\u003e \u003cp\u003e2.9.2 Tests 44\u003c\/p\u003e \u003cp\u003e2.10 Appendix: proofs and complements 45\u003c\/p\u003e \u003cp\u003e2.10.1 Mixtures 45\u003c\/p\u003e \u003cp\u003e2.10.2 Asymptotic normality of M-estimators 46\u003c\/p\u003e \u003cp\u003e2.10.3 Slutsky’s lemma 47\u003c\/p\u003e \u003cp\u003e2.10.4 Quantiles 47\u003c\/p\u003e \u003cp\u003e2.10.5 Alternative algorithms for M-estimators 47\u003c\/p\u003e \u003cp\u003e2.11 Recommendations and software 48\u003c\/p\u003e \u003cp\u003e2.12 Problems 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Measuring Robustness 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The influence function 55\u003c\/p\u003e \u003cp\u003e3.1.1 *The convergence of the SC to the IF 57\u003c\/p\u003e \u003cp\u003e3.2 The breakdown point 58\u003c\/p\u003e \u003cp\u003e3.2.1 Location M-estimators 59\u003c\/p\u003e \u003cp\u003e3.2.2 Scale and dispersion estimators 59\u003c\/p\u003e \u003cp\u003e3.2.3 Location with previously-computed dispersion estimator 60\u003c\/p\u003e \u003cp\u003e3.2.4 Simultaneous estimation 61\u003c\/p\u003e \u003cp\u003e3.2.5 Finite-sample breakdown point 61\u003c\/p\u003e \u003cp\u003e3.3 Maximum asymptotic bias 62\u003c\/p\u003e \u003cp\u003e3.4 Balancing robustness and efficiency 64\u003c\/p\u003e \u003cp\u003e3.5 *“Optimal” robustness 66\u003c\/p\u003e \u003cp\u003e3.5.1 Bias- and variance-optimality of location estimators 66\u003c\/p\u003e \u003cp\u003e3.5.2 Bias optimality of scale and dispersion estimators 66\u003c\/p\u003e \u003cp\u003e3.5.3 The infinitesimal approach 67\u003c\/p\u003e \u003cp\u003e3.5.4 The Hampel approach 68\u003c\/p\u003e \u003cp\u003e3.5.5 Balancing bias and variance: the general problem 70\u003c\/p\u003e \u003cp\u003e3.6 Multidimensional parameters 70\u003c\/p\u003e \u003cp\u003e3.7 *Estimators as functionals 72\u003c\/p\u003e \u003cp\u003e3.8 Appendix: Proofs of results 76\u003c\/p\u003e \u003cp\u003e3.8.1 IF of general M-estimators 76\u003c\/p\u003e \u003cp\u003e3.8.2 Maximum BP of location estimators 76\u003c\/p\u003e \u003cp\u003e3.8.3 BP of location M-estimators 77\u003c\/p\u003e \u003cp\u003e3.8.4 Maximum bias of location M-estimators 79\u003c\/p\u003e \u003cp\u003e3.8.5 The minimax bias property of the median 80\u003c\/p\u003e \u003cp\u003e3.8.6 Minimizing the GES 80\u003c\/p\u003e \u003cp\u003e3.8.7 Hampel optimality 82\u003c\/p\u003e \u003cp\u003e3.9 Problems 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Linear Regression 1 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 87\u003c\/p\u003e \u003cp\u003e4.2 Review of the least squares method 91\u003c\/p\u003e \u003cp\u003e4.3 Classical methods for outlier detection 94\u003c\/p\u003e \u003cp\u003e4.4 Regression M-estimators 97\u003c\/p\u003e \u003cp\u003e4.4.1 M-estimators with known scale 99\u003c\/p\u003e \u003cp\u003e4.4.2 M-estimators with preliminary scale 100\u003c\/p\u003e \u003cp\u003e4.4.3 Simultaneous estimation of regression and scale 102\u003c\/p\u003e \u003cp\u003e4.5 Numerical computing of monotone M-estimators 103\u003c\/p\u003e \u003cp\u003e4.5.1 The L1 estimator 103\u003c\/p\u003e \u003cp\u003e4.5.2 M-estimators with smooth 𝜓-function 104\u003c\/p\u003e \u003cp\u003e4.6 BP of monotone regression estimators 104\u003c\/p\u003e \u003cp\u003e4.7 Robust tests for linear hypothesis 106\u003c\/p\u003e \u003cp\u003e4.7.1 Review of the classical theory 106\u003c\/p\u003e \u003cp\u003e4.7.2 Robust tests using M-estimators 108\u003c\/p\u003e \u003cp\u003e4.8 *Regression quantiles 109\u003c\/p\u003e \u003cp\u003e4.9 Appendix: Proofs and complements 110\u003c\/p\u003e \u003cp\u003e4.9.1 Why equivariance? 110\u003c\/p\u003e \u003cp\u003e4.9.2 Consistency of estimated slopes under asymmetric errors 110\u003c\/p\u003e \u003cp\u003e4.9.3 Maximum FBP of equivariant estimators 111\u003c\/p\u003e \u003cp\u003e4.9.4 The FBP of monotone M-estimators 112\u003c\/p\u003e \u003cp\u003e4.10 Recommendations and software 113\u003c\/p\u003e \u003cp\u003e4.11 Problems 113\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Linear Regression 2 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 115\u003c\/p\u003e \u003cp\u003e5.2 The linear model with random predictors 118\u003c\/p\u003e \u003cp\u003e5.3 M-estimators with a bounded 𝜌-function 119\u003c\/p\u003e \u003cp\u003e5.3.1 Properties of M-estimators with a bounded 𝝆-function 120\u003c\/p\u003e \u003cp\u003e5.4 Estimators based on a robust residual scale 124\u003c\/p\u003e \u003cp\u003e5.4.1 S-estimators 124\u003c\/p\u003e \u003cp\u003e5.4.2 L-estimators of scale and the LTS estimator 126\u003c\/p\u003e \u003cp\u003e5.4.3 𝜏−estimators 127\u003c\/p\u003e \u003cp\u003e5.5 MM-estimators 128\u003c\/p\u003e \u003cp\u003e5.6 Robust inference and variable selection for M-estimators 133\u003c\/p\u003e \u003cp\u003e5.6.1 Bootstrap robust confidence intervals and tests 134\u003c\/p\u003e \u003cp\u003e5.6.2 Variable selection 135\u003c\/p\u003e \u003cp\u003e5.7 Algorithms 138\u003c\/p\u003e \u003cp\u003e5.7.1 Finding local minima 140\u003c\/p\u003e \u003cp\u003e5.7.2 Starting values: the subsampling algorithm 141\u003c\/p\u003e \u003cp\u003e5.7.3 A strategy for faster subsampling-based algorithms 143\u003c\/p\u003e \u003cp\u003e5.7.4 Starting values: the Peña-Yohai estimator 144\u003c\/p\u003e \u003cp\u003e5.7.5 Starting values with numeric and categorical predictors 146\u003c\/p\u003e \u003cp\u003e5.7.6 Comparing initial estimators 149\u003c\/p\u003e \u003cp\u003e5.8 Balancing asymptotic bias and efficiency 150\u003c\/p\u003e \u003cp\u003e5.8.1 “Optimal” redescending M-estimators 153\u003c\/p\u003e \u003cp\u003e5.9 Improving the efficiency of robust regression estimators 155\u003c\/p\u003e \u003cp\u003e5.9.1 Improving efficiency with one-step reweighting 155\u003c\/p\u003e \u003cp\u003e5.9.2 A fully asymptotically efficient one-step procedure 156\u003c\/p\u003e \u003cp\u003e5.9.3 Improving finite-sample efficiency and robustness 158\u003c\/p\u003e \u003cp\u003e5.9.4 Choosing a regression estimator 164\u003c\/p\u003e \u003cp\u003e5.10 Robust regularized regression 164\u003c\/p\u003e \u003cp\u003e5.10.1 Ridge regression 165\u003c\/p\u003e \u003cp\u003e5.10.2 Lasso regression 168\u003c\/p\u003e \u003cp\u003e5.10.3 Other regularized estimators 171\u003c\/p\u003e \u003cp\u003e5.11 *Other estimators 172\u003c\/p\u003e \u003cp\u003e5.11.1 Generalized M-estimators 172\u003c\/p\u003e \u003cp\u003e5.11.2 Projection estimators 174\u003c\/p\u003e \u003cp\u003e5.11.3 Constrained M-estimators 175\u003c\/p\u003e \u003cp\u003e5.11.4 Maximum depth estimators 175\u003c\/p\u003e \u003cp\u003e5.12 Other topics 176\u003c\/p\u003e \u003cp\u003e5.12.1 The exact fit property 176\u003c\/p\u003e \u003cp\u003e5.12.2 Heteroskedastic errors 177\u003c\/p\u003e \u003cp\u003e5.12.3 A robust multiple correlation coefficient 180\u003c\/p\u003e \u003cp\u003e5.13 *Appendix: proofs and complements 182\u003c\/p\u003e \u003cp\u003e5.13.1 The BP of monotone M-estimators with random X 182\u003c\/p\u003e \u003cp\u003e5.13.2 Heavy-tailed x 183\u003c\/p\u003e \u003cp\u003e5.13.3 Proof of the exact fit property 183\u003c\/p\u003e \u003cp\u003e5.13.4 The BP of S-estimators 184\u003c\/p\u003e \u003cp\u003e5.13.5 Asymptotic bias of M-estimators 186\u003c\/p\u003e \u003cp\u003e5.13.6 Hampel optimality for GM-estimators 187\u003c\/p\u003e \u003cp\u003e5.13.7 Justification of RFPE∗ 188\u003c\/p\u003e \u003cp\u003e5.14 Recommendations and software 191\u003c\/p\u003e \u003cp\u003e5.15 Problems 191\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Multivariate Analysis 195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 195\u003c\/p\u003e \u003cp\u003e6.2 Breakdown and efficiency of multivariate estimators 200\u003c\/p\u003e \u003cp\u003e6.2.1 Breakdown point 200\u003c\/p\u003e \u003cp\u003e6.2.2 The multivariate exact fit property 201\u003c\/p\u003e \u003cp\u003e6.2.3 Efficiency 201\u003c\/p\u003e \u003cp\u003e6.3 M-estimators 202\u003c\/p\u003e \u003cp\u003e6.3.1 Collinearity 205\u003c\/p\u003e \u003cp\u003e6.3.2 Size and shape 205\u003c\/p\u003e \u003cp\u003e6.3.3 Breakdown point 206\u003c\/p\u003e \u003cp\u003e6.4 Estimators based on a robust scale 207\u003c\/p\u003e \u003cp\u003e6.4.1 The minimum volume ellipsoid estimator 208\u003c\/p\u003e \u003cp\u003e6.4.2 S-estimators 208\u003c\/p\u003e \u003cp\u003e6.4.3 The MCD estimator 210\u003c\/p\u003e \u003cp\u003e6.4.4 S-estimators for high dimension 210\u003c\/p\u003e \u003cp\u003e6.4.5 𝜏-estimators 214\u003c\/p\u003e \u003cp\u003e6.4.6 One-step reweighting 215\u003c\/p\u003e \u003cp\u003e6.5 MM-estimators 215\u003c\/p\u003e \u003cp\u003e6.6 The Stahel–Donoho estimator 217\u003c\/p\u003e \u003cp\u003e6.7 Asymptotic bias 219\u003c\/p\u003e \u003cp\u003e6.8 Numerical computing of multivariate estimators 220\u003c\/p\u003e \u003cp\u003e6.8.1 Monotone M-estimators 220\u003c\/p\u003e \u003cp\u003e6.8.2 Local solutions for S-estimators 221\u003c\/p\u003e \u003cp\u003e6.8.3 Subsampling for estimators based on a robust scale 221\u003c\/p\u003e \u003cp\u003e6.8.4 The MVE 223\u003c\/p\u003e \u003cp\u003e6.8.5 Computation of S-estimators 223\u003c\/p\u003e \u003cp\u003e6.8.6 The MCD 223\u003c\/p\u003e \u003cp\u003e6.8.7 The Stahel–Donoho estimator 224\u003c\/p\u003e \u003cp\u003e6.9 Faster robust scatter matrix estimators 224\u003c\/p\u003e \u003cp\u003e6.9.1 Using pairwise robust covariances 224\u003c\/p\u003e \u003cp\u003e6.9.2 The Peña–Prieto procedure 228\u003c\/p\u003e \u003cp\u003e6.10 Choosing a location\/scatter estimator 229\u003c\/p\u003e \u003cp\u003e6.10.1 Efficiency 230\u003c\/p\u003e \u003cp\u003e6.10.2 Behavior under contamination 231\u003c\/p\u003e \u003cp\u003e6.10.3 Computing times 232\u003c\/p\u003e \u003cp\u003e6.10.4 Tuning constants 233\u003c\/p\u003e \u003cp\u003e6.10.5 Conclusions 233\u003c\/p\u003e \u003cp\u003e6.11 Robust principal components 234\u003c\/p\u003e \u003cp\u003e6.11.1 Spherical principal components 236\u003c\/p\u003e \u003cp\u003e6.11.2 Robust PCA based on a robust scale 237\u003c\/p\u003e \u003cp\u003e6.12 Estimation of multivariate scatter and location with missing data 240\u003c\/p\u003e \u003cp\u003e6.12.1 Notation 240\u003c\/p\u003e \u003cp\u003e6.12.2 GS estimators for missing data 241\u003c\/p\u003e \u003cp\u003e6.13 Robust estimators under the cellwise contamination model 242\u003c\/p\u003e \u003cp\u003e6.14 Regularized robust estimators of the inverse of the covariance matrix 245\u003c\/p\u003e \u003cp\u003e6.15 Mixed linear models 246\u003c\/p\u003e \u003cp\u003e6.15.1 Robust estimation for MLM 248\u003c\/p\u003e \u003cp\u003e6.15.2 Breakdown point of MLM estimators 248\u003c\/p\u003e \u003cp\u003e6.15.3 S-estimators for MLMs 250\u003c\/p\u003e \u003cp\u003e6.15.4 Composite 𝜏-estimators 250\u003c\/p\u003e \u003cp\u003e6.16 *Other estimators of location and scatter 254\u003c\/p\u003e \u003cp\u003e6.16.1 Projection estimators 254\u003c\/p\u003e \u003cp\u003e6.16.2 Constrained M-estimators 255\u003c\/p\u003e \u003cp\u003e6.16.3 Multivariate depth 256\u003c\/p\u003e \u003cp\u003e6.17 Appendix: proofs and complements 256\u003c\/p\u003e \u003cp\u003e6.17.1 Why affine equivariance? 256\u003c\/p\u003e \u003cp\u003e6.17.2 Consistency of equivariant estimators 256\u003c\/p\u003e \u003cp\u003e6.17.3 The estimating equations of the MLE 257\u003c\/p\u003e \u003cp\u003e6.17.4 Asymptotic BP of monotone M-estimators 258\u003c\/p\u003e \u003cp\u003e6.17.5 The estimating equations for S-estimators 260\u003c\/p\u003e \u003cp\u003e6.17.6 Behavior of S-estimators for high p 261\u003c\/p\u003e \u003cp\u003e6.17.7 Calculating the asymptotic covariance matrix of location M-estimators 262\u003c\/p\u003e \u003cp\u003e6.17.8 The exact fit property 263\u003c\/p\u003e \u003cp\u003e6.17.9 Elliptical distributions 264\u003c\/p\u003e \u003cp\u003e6.17.10 Consistency of Gnanadesikan–Kettenring correlations 265\u003c\/p\u003e \u003cp\u003e6.17.11 Spherical principal components 266\u003c\/p\u003e \u003cp\u003e6.17.12 Fixed point estimating equations and computing algorithm for the GS estimator 267\u003c\/p\u003e \u003cp\u003e6.18 Recommendations and software 268\u003c\/p\u003e \u003cp\u003e6.19 Problems 269\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generalized Linear Models 271\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Binary response regression 271\u003c\/p\u003e \u003cp\u003e7.2 Robust estimators for the logistic model 275\u003c\/p\u003e \u003cp\u003e7.2.1 Weighted MLEs 275\u003c\/p\u003e \u003cp\u003e7.2.2 Redescending M-estimators 276\u003c\/p\u003e \u003cp\u003e7.3 Generalized linear models 281\u003c\/p\u003e \u003cp\u003e7.3.1 Conditionally unbiased bounded influence estimators 283\u003c\/p\u003e \u003cp\u003e7.4 Transformed M-estimators 284\u003c\/p\u003e \u003cp\u003e7.4.1 Definition of transformed M-estimators 284\u003c\/p\u003e \u003cp\u003e7.4.2 Some examples of variance-stabilizing transformations 286\u003c\/p\u003e \u003cp\u003e7.4.3 Other estimators for GLMs 286\u003c\/p\u003e \u003cp\u003e7.5 Recommendations and software 289\u003c\/p\u003e \u003cp\u003e7.6 Problems 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Time Series 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Time series outliers and their impact 294\u003c\/p\u003e \u003cp\u003e8.1.1 Simple examples of outliers influence 296\u003c\/p\u003e \u003cp\u003e8.1.2 Probability models for time series outliers 298\u003c\/p\u003e \u003cp\u003e8.1.3 Bias impact of AOs 301\u003c\/p\u003e \u003cp\u003e8.2 Classical estimators for AR models 302\u003c\/p\u003e \u003cp\u003e8.2.1 The Durbin–Levinson algorithm 305\u003c\/p\u003e \u003cp\u003e8.2.2 Asymptotic distribution of classical estimators 307\u003c\/p\u003e \u003cp\u003e8.3 Classical estimators for ARMA models 308\u003c\/p\u003e \u003cp\u003e8.4 M-estimators of ARMA models 310\u003c\/p\u003e \u003cp\u003e8.4.1 M-estimators and their asymptotic distribution 310\u003c\/p\u003e \u003cp\u003e8.4.2 The behavior of M-estimators in AR processes with additive outliers 311\u003c\/p\u003e \u003cp\u003e8.4.3 The behavior of LS and M-estimators for ARMA processes with infinite innovation variance 312\u003c\/p\u003e \u003cp\u003e8.5 Generalized M-estimators 313\u003c\/p\u003e \u003cp\u003e8.6 Robust AR estimation using robust filters 315\u003c\/p\u003e \u003cp\u003e8.6.1 Naive minimum robust scale autoregression estimators 315\u003c\/p\u003e \u003cp\u003e8.6.2 The robust filter algorithm 316\u003c\/p\u003e \u003cp\u003e8.6.3 Minimum robust scale estimators based on robust filtering 318\u003c\/p\u003e \u003cp\u003e8.6.4 A robust Durbin–Levinson algorithm 319\u003c\/p\u003e \u003cp\u003e8.6.5 Choice of scale for the robust Durbin–Levinson procedure 320\u003c\/p\u003e \u003cp\u003e8.6.6 Robust identification of AR order 320\u003c\/p\u003e \u003cp\u003e8.7 Robust model identification 321\u003c\/p\u003e \u003cp\u003e8.8 Robust ARMA model estimation using robust filters 324\u003c\/p\u003e \u003cp\u003e8.8.1 𝜏-estimators of ARMA models 324\u003c\/p\u003e \u003cp\u003e8.8.2 Robust filters for ARMA models 326\u003c\/p\u003e \u003cp\u003e8.8.3 Robustly filtered 𝜏-estimators 328\u003c\/p\u003e \u003cp\u003e8.9 ARIMA and SARIMA models 329\u003c\/p\u003e \u003cp\u003e8.10 Detecting time series outliers and level shifts 333\u003c\/p\u003e \u003cp\u003e8.10.1 Classical detection of time series outliers and level shifts 334\u003c\/p\u003e \u003cp\u003e8.10.2 Robust detection of outliers and level shifts for ARIMA models 336\u003c\/p\u003e \u003cp\u003e8.10.3 REGARIMA models: estimation and outlier detection 338\u003c\/p\u003e \u003cp\u003e8.11 Robustness measures for time series 340\u003c\/p\u003e \u003cp\u003e8.11.1 Influence function 340\u003c\/p\u003e \u003cp\u003e8.11.2 Maximum bias 342\u003c\/p\u003e \u003cp\u003e8.11.3 Breakdown point 343\u003c\/p\u003e \u003cp\u003e8.11.4 Maximum bias curves for the AR (1) model 343\u003c\/p\u003e \u003cp\u003e8.12 Other approaches for ARMA models 345\u003c\/p\u003e \u003cp\u003e8.12.1 Estimators based on robust autocovariances 345\u003c\/p\u003e \u003cp\u003e8.12.2 Estimators based on memory-m prediction residuals 346\u003c\/p\u003e \u003cp\u003e8.13 High-efficiency robust location estimators 347\u003c\/p\u003e \u003cp\u003e8.14 Robust spectral density estimation 348\u003c\/p\u003e \u003cp\u003e8.14.1 Definition of the spectral density 348\u003c\/p\u003e \u003cp\u003e8.14.2 AR spectral density 349\u003c\/p\u003e \u003cp\u003e8.14.3 Classic spectral density estimation methods 349\u003c\/p\u003e \u003cp\u003e8.14.4 Prewhitening 350\u003c\/p\u003e \u003cp\u003e8.14.5 Influence of outliers on spectral density estimators 351\u003c\/p\u003e \u003cp\u003e8.14.6 Robust spectral density estimation 353\u003c\/p\u003e \u003cp\u003e8.14.7 Robust time-average spectral density estimator 354\u003c\/p\u003e \u003cp\u003e8.15 Appendix A: Heuristic derivation of the asymptotic distribution of M-estimators for ARMA models 356\u003c\/p\u003e \u003cp\u003e8.16 Appendix B: Robust filter covariance recursions 359\u003c\/p\u003e \u003cp\u003e8.17 Appendix C: ARMA model state-space representation 360\u003c\/p\u003e \u003cp\u003e8.18 Recommendations and software 361\u003c\/p\u003e \u003cp\u003e8.19 Problems 361\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Numerical Algorithms 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Regression M-estimators 363\u003c\/p\u003e \u003cp\u003e9.2 Regression S-estimators 366\u003c\/p\u003e \u003cp\u003e9.3 The LTS-estimator 366\u003c\/p\u003e \u003cp\u003e9.4 Scale M-estimators 367\u003c\/p\u003e \u003cp\u003e9.4.1 Convergence of the fixed-point algorithm 367\u003c\/p\u003e \u003cp\u003e9.4.2 Algorithms for the non-concave case 368\u003c\/p\u003e \u003cp\u003e9.5 Multivariate M-estimators 369\u003c\/p\u003e \u003cp\u003e9.6 Multivariate S-estimators 370\u003c\/p\u003e \u003cp\u003e9.6.1 S-estimators with monotone weights 370\u003c\/p\u003e \u003cp\u003e9.6.2 The MCD 371\u003c\/p\u003e \u003cp\u003e9.6.3 S-estimators with non-monotone weights 371\u003c\/p\u003e \u003cp\u003e9.6.4 *Proof of (9.27) 372\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Asymptotic Theory of M-estimators 373\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Existence and uniqueness of solutions 374\u003c\/p\u003e \u003cp\u003e10.1.1 Redescending location estimators 375\u003c\/p\u003e \u003cp\u003e10.2 Consistency 376\u003c\/p\u003e \u003cp\u003e10.3 Asymptotic normality 377\u003c\/p\u003e \u003cp\u003e10.4 Convergence of the SC to the IF 379\u003c\/p\u003e \u003cp\u003e10.5 M-estimators of several parameters 381\u003c\/p\u003e \u003cp\u003e10.6 Location M-estimators with preliminary scale 384\u003c\/p\u003e \u003cp\u003e10.7 Trimmed means 386\u003c\/p\u003e \u003cp\u003e10.8 Optimality of the MLE 386\u003c\/p\u003e \u003cp\u003e10.9 Regression M-estimators: existence and uniqueness 388\u003c\/p\u003e \u003cp\u003e10.10 Regression M-estimators: asymptotic normality 389\u003c\/p\u003e \u003cp\u003e10.10.1 Fixed X 389\u003c\/p\u003e \u003cp\u003e10.10.2 Asymptotic normality: random X 394\u003c\/p\u003e \u003cp\u003e10.11 Regression M estimators: Fisher-consistency 394\u003c\/p\u003e \u003cp\u003e10.11.1 Redescending estimators 394\u003c\/p\u003e \u003cp\u003e10.11.2 Monotone estimators 396\u003c\/p\u003e \u003cp\u003e10.12 Nonexistence of moments of the sample median 398\u003c\/p\u003e \u003cp\u003e10.13 Problems 399\u003c\/p\u003e \u003cp\u003e11 Description of Datasets 401\u003c\/p\u003e \u003cp\u003eReferences 407\u003c\/p\u003e \u003cp\u003eIndex 423\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407008964951,"sku":"9781119214687","price":66.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119214687.jpg?v=1730497870","url":"https:\/\/bookcurl.com\/products\/robust-statistics-theory-and-methods-with-r-second-edition-9781119214687","provider":"Book Curl","version":"1.0","type":"link"}