Autore	Huber Peter J
Pubbl/distr/stampa	New York, : Wiley, c1981
Descrizione fisica	1 online resource (327 p.)
Disciplina	519.5
Collana	Wiley series in probability and mathematical statistics
Soggetto topico	Robust statistics Mathematical statistics
ISBN	1-280-27335-6 9786610273355 0-471-72524-2 0-471-72525-0
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Robust Statistics; Contents; 1 GENERALITIES; 2 THE WEAK TOPOLOGY AND ITS METRIZATION; 3 THE BASIC TYPES OF ESTIMATES; 4 ASYMPTOTIC MINIMAX THEORY FOR ESTIMATING A LOCATION PARAMETER; 5 SCALE ESTIMATES; 6 MULTIPARAMETER PROBLEMS, IN PARTICULAR JOINT ESTIMATION OF LOCATION AND SCALE; 7 REGRESSION; 8 ROBUST COVARIANCE AND CORRELATION MATRICES; 9 ROBUSTNESS OF DESIGN; 10 EXACT FINITE SAMPLE RESULTS; 11 MISCELLANEOUS TOPICS; REFERENCES; INDEX;
Record Nr.	UNISA-996213319303316

Autore	Huber, Peter J.
Edizione	[2nd ed.]
Pubbl/distr/stampa	Hoboken, N.J. : Wiley, c2009
Descrizione fisica	xvi, 354 p. : ill. ; 25 cm
Disciplina	519.5
Altri autori (Persone)	Ronchetti, Elvezio
Collana	Wiley series in probability and statistics
Soggetto topico	Robust statistics
ISBN	9780470129906
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Record Nr.	UNISALENTO-991000631499707536

Autore	Maronna Ricardo A.
Edizione	[Second edition.]
Pubbl/distr/stampa	Hoboken, New Jersey : , : WIley, , 2019
Descrizione fisica	1 online resource (431 pages)
Disciplina	519.5
Collana	Wiley series in probability and statistics
Soggetto topico	Robust statistics
Soggetto genere / forma	Electronic books.
ISBN	1-119-21467-X 1-119-21466-1 1-119-21465-3
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Note: sections marked with an asterisk can be skipped on first reading -- Preface xv -- Preface to the First Edition xxi -- About the Companion Website xxix -- 1 Introduction 1 -- 1.1 Classical and robust approaches to statistics 1 -- 1.2 Mean and standard deviation 2 -- 1.3 The “three sigma edit” rule 6 -- 1.4 Linear regression 8 -- 1.4.1 Straight-line regression 8 -- 1.4.2 Multiple linear regression 9 -- 1.5 Correlation coefficients 12 -- 1.6 Other parametric models 13 -- 1.7 Problems 16 -- 2 Location and Scale 17 -- 2.1 The location model 17 -- 2.2 Formalizing departures from normality 19 -- 2.3 M-estimators of location 22 -- 2.3.1 Generalizing maximum likelihood 22 -- 2.3.2 The distribution of M-estimators 25 -- 2.3.3 An intuitive view of M-estimators 28 -- 2.3.4 Redescending M-estimators 29 -- 2.4 Trimmed and Winsorized means 31 -- 2.5 M-estimators of scale 33 -- 2.6 Dispersion estimators 35 -- 2.7 M-estimators of location with unknown dispersion 37 -- 2.7.1 Previous estimation of dispersion 38 -- 2.7.2 Simultaneous M-estimators of location and dispersion 38 -- 2.8 Numerical computing of M-estimators 40 -- 2.8.1 Location with previously-computed dispersion estimation 40 -- 2.8.2 Scale estimators 41 -- 2.8.3 Simultaneous estimation of location and dispersion 42 -- 2.9 Robust confidence intervals and tests 42 -- 2.9.1 Confidence intervals 42 -- 2.9.2 Tests 44 -- 2.10 Appendix: proofs and complements 45 -- 2.10.1 Mixtures 45 -- 2.10.2 Asymptotic normality of M-estimators 46 -- 2.10.3 Slutsky’s lemma 47 -- 2.10.4 Quantiles 47 -- 2.10.5 Alternative algorithms for M-estimators 47 -- 2.11 Recommendations and software 48 -- 2.12 Problems 49 -- 3 Measuring Robustness 51 -- 3.1 The influence function 55 -- 3.1.1 The convergence of the SC to the IF 57 -- 3.2 The breakdown point 58 -- 3.2.1 Location M-estimators 59 -- 3.2.2 Scale and dispersion estimators 59 -- 3.2.3 Location with previously-computed dispersion estimator 60 -- 3.2.4 Simultaneous estimation 61. 3.2.5 Finite-sample breakdown point 61 -- 3.3 Maximum asymptotic bias 62 -- 3.4 Balancing robustness and efficiency 64 -- 3.5 “Optimal” robustness 66 -- 3.5.1 Bias- and variance-optimality of location estimators 66 -- 3.5.2 Bias optimality of scale and dispersion estimators 66 -- 3.5.3 The infinitesimal approach 67 -- 3.5.4 The Hampel approach 68 -- 3.5.5 Balancing bias and variance: the general problem 70 -- 3.6 Multidimensional parameters 70 -- 3.7 Estimators as functionals 72 -- 3.8 Appendix: Proofs of results 76 -- 3.8.1 IF of general M-estimators 76 -- 3.8.2 Maximum BP of location estimators 76 -- 3.8.3 BP of location M-estimators 77 -- 3.8.4 Maximum bias of location M-estimators 79 -- 3.8.5 The minimax bias property of the median 80 -- 3.8.6 Minimizing the GES 80 -- 3.8.7 Hampel optimality 82 -- 3.9 Problems 85 -- 4 Linear Regression 1 87 -- 4.1 Introduction 87 -- 4.2 Review of the least squares method 91 -- 4.3 Classical methods for outlier detection 94 -- 4.4 Regression M-estimators 97 -- 4.4.1 M-estimators with known scale 99 -- 4.4.2 M-estimators with preliminary scale 100 -- 4.4.3 Simultaneous estimation of regression and scale 102 -- 4.5 Numerical computing of monotone M-estimators 103 -- 4.5.1 The L1 estimator 103 -- 4.5.2 M-estimators with smooth 𝜓-function 104 -- 4.6 BP of monotone regression estimators 104 -- 4.7 Robust tests for linear hypothesis 106 -- 4.7.1 Review of the classical theory 106 -- 4.7.2 Robust tests using M-estimators 108 -- 4.8 Regression quantiles 109 -- 4.9 Appendix: Proofs and complements 110 -- 4.9.1 Why equivariance? 110 -- 4.9.2 Consistency of estimated slopes under asymmetric errors 110 -- 4.9.3 Maximum FBP of equivariant estimators 111 -- 4.9.4 The FBP of monotone M-estimators 112 -- 4.10 Recommendations and software 113 -- 4.11 Problems 113 -- 5 Linear Regression 2 115 -- 5.1 Introduction 115 -- 5.2 The linear model with random predictors 118 -- 5.3 M-estimators with a bounded 𝜌-function 119. 5.3.1 Properties of M-estimators with a bounded 𝝆-function 120 -- 5.4 Estimators based on a robust residual scale 124 -- 5.4.1 S-estimators 124 -- 5.4.2 L-estimators of scale and the LTS estimator 126 -- 5.4.3 𝜏−estimators 127 -- 5.5 MM-estimators 128 -- 5.6 Robust inference and variable selection for M-estimators 133 -- 5.6.1 Bootstrap robust confidence intervals and tests 134 -- 5.6.2 Variable selection 135 -- 5.7 Algorithms 138 -- 5.7.1 Finding local minima 140 -- 5.7.2 Starting values: the subsampling algorithm 141 -- 5.7.3 A strategy for faster subsampling-based algorithms 143 -- 5.7.4 Starting values: the Peña-Yohai estimator 144 -- 5.7.5 Starting values with numeric and categorical predictors 146 -- 5.7.6 Comparing initial estimators 149 -- 5.8 Balancing asymptotic bias and efficiency 150 -- 5.8.1 “Optimal” redescending M-estimators 153 -- 5.9 Improving the efficiency of robust regression estimators 155 -- 5.9.1 Improving efficiency with one-step reweighting 155 -- 5.9.2 A fully asymptotically efficient one-step procedure 156 -- 5.9.3 Improving finite-sample efficiency and robustness 158 -- 5.9.4 Choosing a regression estimator 164 -- 5.10 Robust regularized regression 164 -- 5.10.1 Ridge regression 165 -- 5.10.2 Lasso regression 168 -- 5.10.3 Other regularized estimators 171 -- 5.11 Other estimators 172 -- 5.11.1 Generalized M-estimators 172 -- 5.11.2 Projection estimators 174 -- 5.11.3 Constrained M-estimators 175 -- 5.11.4 Maximum depth estimators 175 -- 5.12 Other topics 176 -- 5.12.1 The exact fit property 176 -- 5.12.2 Heteroskedastic errors 177 -- 5.12.3 A robust multiple correlation coefficient 180 -- 5.13 Appendix: proofs and complements 182 -- 5.13.1 The BP of monotone M-estimators with random X 182 -- 5.13.2 Heavy-tailed x 183 -- 5.13.3 Proof of the exact fit property 183 -- 5.13.4 The BP of S-estimators 184 -- 5.13.5 Asymptotic bias of M-estimators 186 -- 5.13.6 Hampel optimality for GM-estimators 187 -- 5.13.7 Justification of RFPE∗ 188. 5.14 Recommendations and software 191 -- 5.15 Problems 191 -- 6 Multivariate Analysis 195 -- 6.1 Introduction 195 -- 6.2 Breakdown and efficiency of multivariate estimators 200 -- 6.2.1 Breakdown point 200 -- 6.2.2 The multivariate exact fit property 201 -- 6.2.3 Efficiency 201 -- 6.3 M-estimators 202 -- 6.3.1 Collinearity 205 -- 6.3.2 Size and shape 205 -- 6.3.3 Breakdown point 206 -- 6.4 Estimators based on a robust scale 207 -- 6.4.1 The minimum volume ellipsoid estimator 208 -- 6.4.2 S-estimators 208 -- 6.4.3 The MCD estimator 210 -- 6.4.4 S-estimators for high dimension 210 -- 6.4.5 𝜏-estimators 214 -- 6.4.6 One-step reweighting 215 -- 6.5 MM-estimators 215 -- 6.6 The Stahel-Donoho estimator 217 -- 6.7 Asymptotic bias 219 -- 6.8 Numerical computing of multivariate estimators 220 -- 6.8.1 Monotone M-estimators 220 -- 6.8.2 Local solutions for S-estimators 221 -- 6.8.3 Subsampling for estimators based on a robust scale 221 -- 6.8.4 The MVE 223 -- 6.8.5 Computation of S-estimators 223 -- 6.8.6 The MCD 223 -- 6.8.7 The Stahel-Donoho estimator 224 -- 6.9 Faster robust scatter matrix estimators 224 -- 6.9.1 Using pairwise robust covariances 224 -- 6.9.2 The Peña-Prieto procedure 228 -- 6.10 Choosing a location/scatter estimator 229 -- 6.10.1 Efficiency 230 -- 6.10.2 Behavior under contamination 231 -- 6.10.3 Computing times 232 -- 6.10.4 Tuning constants 233 -- 6.10.5 Conclusions 233 -- 6.11 Robust principal components 234 -- 6.11.1 Spherical principal components 236 -- 6.11.2 Robust PCA based on a robust scale 237 -- 6.12 Estimation of multivariate scatter and location with missing data 240 -- 6.12.1 Notation 240 -- 6.12.2 GS estimators for missing data 241 -- 6.13 Robust estimators under the cellwise contamination model 242 -- 6.14 Regularized robust estimators of the inverse of the covariance matrix 245 -- 6.15 Mixed linear models 246 -- 6.15.1 Robust estimation for MLM 248 -- 6.15.2 Breakdown point of MLM estimators 248 -- 6.15.3 S-estimators for MLMs 250. 6.15.4 Composite 𝜏-estimators 250 -- 6.16 Other estimators of location and scatter 254 -- 6.16.1 Projection estimators 254 -- 6.16.2 Constrained M-estimators 255 -- 6.16.3 Multivariate depth 256 -- 6.17 Appendix: proofs and complements 256 -- 6.17.1 Why affine equivariance? 256 -- 6.17.2 Consistency of equivariant estimators 256 -- 6.17.3 The estimating equations of the MLE 257 -- 6.17.4 Asymptotic BP of monotone M-estimators 258 -- 6.17.5 The estimating equations for S-estimators 260 -- 6.17.6 Behavior of S-estimators for high p 261 -- 6.17.7 Calculating the asymptotic covariance matrix of location M-estimators 262 -- 6.17.8 The exact fit property 263 -- 6.17.9 Elliptical distributions 264 -- 6.17.10 Consistency of Gnanadesikan-Kettenring correlations 265 -- 6.17.11 Spherical principal components 266 -- 6.17.12 Fixed point estimating equations and computing algorithm for the GS estimator 267 -- 6.18 Recommendations and software 268 -- 6.19 Problems 269 -- 7 Generalized Linear Models 271 -- 7.1 Binary response regression 271 -- 7.2 Robust estimators for the logistic model 275 -- 7.2.1 Weighted MLEs 275 -- 7.2.2 Redescending M-estimators 276 -- 7.3 Generalized linear models 281 -- 7.3.1 Conditionally unbiased bounded influence estimators 283 -- 7.4 Transformed M-estimators 284 -- 7.4.1 Definition of transformed M-estimators 284 -- 7.4.2 Some examples of variance-stabilizing transformations 286 -- 7.4.3 Other estimators for GLMs 286 -- 7.5 Recommendations and software 289 -- 7.6 Problems 290 -- 8 Time Series 293 -- 8.1 Time series outliers and their impact 294 -- 8.1.1 Simple examples of outliers influence 296 -- 8.1.2 Probability models for time series outliers 298 -- 8.1.3 Bias impact of AOs 301 -- 8.2 Classical estimators for AR models 302 -- 8.2.1 The Durbin-Levinson algorithm 305 -- 8.2.2 Asymptotic distribution of classical estimators 307 -- 8.3 Classical estimators for ARMA models 308 -- 8.4 M-estimators of ARMA models 310 -- 8.4.1 M-estimators and their asymptotic distribution 310. 8.4.2 The behavior of M-estimators in AR processes with additive outliers 311 -- 8.4.3 The behavior of LS and M-estimators for ARMA processes with infinite innovation variance 312 -- 8.5 Generalized M-estimators 313 -- 8.6 Robust AR estimation using robust filters 315 -- 8.6.1 Naive minimum robust scale autoregression estimators 315 -- 8.6.2 The robust filter algorithm 316 -- 8.6.3 Minimum robust scale estimators based on robust filtering 318 -- 8.6.4 A robust Durbin-Levinson algorithm 319 -- 8.6.5 Choice of scale for the robust Durbin-Levinson procedure 320 -- 8.6.6 Robust identification of AR order 320 -- 8.7 Robust model identification 321 -- 8.8 Robust ARMA model estimation using robust filters 324 -- 8.8.1 𝜏-estimators of ARMA models 324 -- 8.8.2 Robust filters for ARMA models 326 -- 8.8.3 Robustly filtered 𝜏-estimators 328 -- 8.9 ARIMA and SARIMA models 329 -- 8.10 Detecting time series outliers and level shifts 333 -- 8.10.1 Classical detection of time series outliers and level shifts 334 -- 8.10.2 Robust detection of outliers and level shifts for ARIMA models 336 -- 8.10.3 REGARIMA models: estimation and outlier detection 338 -- 8.11 Robustness measures for time series 340 -- 8.11.1 Influence function 340 -- 8.11.2 Maximum bias 342 -- 8.11.3 Breakdown point 343 -- 8.11.4 Maximum bias curves for the AR (1) model 343 -- 8.12 Other approaches for ARMA models 345 -- 8.12.1 Estimators based on robust autocovariances 345 -- 8.12.2 Estimators based on memory-m prediction residuals 346 -- 8.13 High-efficiency robust location estimators 347 -- 8.14 Robust spectral density estimation 348 -- 8.14.1 Definition of the spectral density 348 -- 8.14.2 AR spectral density 349 -- 8.14.3 Classic spectral density estimation methods 349 -- 8.14.4 Prewhitening 350 -- 8.14.5 Influence of outliers on spectral density estimators 351 -- 8.14.6 Robust spectral density estimation 353 -- 8.14.7 Robust time-average spectral density estimator 354 -- 8.15 Appendix A: Heuristic derivation of the asymptotic distribution of M-estimators for ARMA models 356. 8.16 Appendix B: Robust filter covariance recursions 359 -- 8.17 Appendix C: ARMA model state-space representation 360 -- 8.18 Recommendations and software 361 -- 8.19 Problems 361 -- 9 Numerical Algorithms 363 -- 9.1 Regression M-estimators 363 -- 9.2 Regression S-estimators 366 -- 9.3 The LTS-estimator 366 -- 9.4 Scale M-estimators 367 -- 9.4.1 Convergence of the fixed-point algorithm 367 -- 9.4.2 Algorithms for the non-concave case 368 -- 9.5 Multivariate M-estimators 369 -- 9.6 Multivariate S-estimators 370 -- 9.6.1 S-estimators with monotone weights 370 -- 9.6.2 The MCD 371 -- 9.6.3 S-estimators with non-monotone weights 371 -- 9.6.4 Proof of (9.27) 372 -- 10 Asymptotic Theory of M-estimators 373 -- 10.1 Existence and uniqueness of solutions 374 -- 10.1.1 Redescending location estimators 375 -- 10.2 Consistency 376 -- 10.3 Asymptotic normality 377 -- 10.4 Convergence of the SC to the IF 379 -- 10.5 M-estimators of several parameters 381 -- 10.6 Location M-estimators with preliminary scale 384 -- 10.7 Trimmed means 386 -- 10.8 Optimality of the MLE 386 -- 10.9 Regression M-estimators: existence and uniqueness 388 -- 10.10 Regression M-estimators: asymptotic normality 389 -- 10.10.1 Fixed X 389 -- 10.10.2 Asymptotic normality: random X 394 -- 10.11 Regression M estimators: Fisher-consistency 394 -- 10.11.1 Redescending estimators 394 -- 10.11.2 Monotone estimators 396 -- 10.12 Nonexistence of moments of the sample median 398 -- 10.13 Problems 399 -- 11 Description of Datasets 401 -- References 407 -- Index 423.
Record Nr.	UNINA-9910467366703321

Pubbl/distr/stampa	New York, : Wiley, 1986
Descrizione fisica	1 online resource (538 p.)
Disciplina	519.5 519.54
Altri autori (Persone)	HampelFrank R. <1941->
Collana	Wiley series in probability and statistics
Soggetto topico	Robust statistics
Soggetto genere / forma	Electronic books.
ISBN	1-283-33237-X 9786613332370 1-118-18643-5 1-118-15068-6
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Robust Statistics: The Approach Based on Influence Functions; Contents; 1. INTRODUCTION AND MOTIVATION; 1.1. The Place and Aims of Robust Statistics; 1.1a. What Is Robust Statistics?; 1.1b. The Relation to Some Other Key Words in Statistics; 1.1c. The Aims of Robust Statistics; 1.1d. An Example; 1.2. Why Robust Statistics?; 1.2a. The Role of Parametric Models; 1.2b. Types of Deviations from Parametric Models; 1.2c. The Frequency of Gross Errors; 1.2d. The Effects of Mild Deviations from a Parametric Model; 1.2e. How Necessary Are Robust Procedures? 1.3. The Main Approaches towards a Theory of Robustness1.3a. Some Historical Notes; 1.3b. Huber's Minimax Approach for Robust Estimation; 1.3c. Huber's Second Approach to Robust Statistics via Robustifed Likelihood Ratio Tests; 1.3d. The Approach Based on In Juence Functions; 1.3e. The Relation between the Minimax Approach and the Approach Based on Influence Functions; 1.3f. The Approach Based on Influence Functions as a Robustifed Likelihood Approach, and Its Relation to Various Statistical Schools; 1.4. Rejection of Outliers and Robust Statistics; 1.4a. Why Rejection of Outliers? 1.4b. How Well Are Objective and Subjective Methods for the Rejection of Outliers Doing in the Context of Robust Estimation?Exercises and Problems; 2. ONE-DIMENSIONAL ESTIMATORS; 2.0. An Introductory Example; 2.1. The Influence Function; 2.1a. Parametric Models, Estimators, and Functionals; 2.1b. Definition and Properties of the Influence Function; 2.1c. Robustness Measures Derived from the Influence Function; 2.1d. Some Simple Examples; 2.1e. Finite-Sample Versions; 2.2. The Breakdown Point and Qualitative Robustness; 2.2a. Global Reliability: The Breakdown Point 2.2b. Continuity and Qualitative Robustness2.3. Classes of Estimators; 2.3a. M-Estimators; 2.3b. L-Estimators; 2.3c. R-Estimators; 2.3d. Other Types of Estimators: A, D, P, S, W; 2.4. Optimally Bounding the Gross-Error Sensitivity; 2.4a. The General Optimality Result; 2.4b. M-Estimator; 2.4c. L-Estimators; 2.4d. R-Estimators; 2.5. The Change-of-Variance Function; 2.5a. Definitions; 2.5b. B-Robustness versus V-Robustness; 2.5c. The Most Robust Estimator; 2.5d. Optimal Robust Estimators; 2.5e. M-Estimators for Scale; 2.5f. Further Topics; 2.6. Redescending M-Estimators; 2.6a. Introduction 2.6b. Most Robust Estimators2.6c. Optimal Robust Estimators; 2.6d. Schematic Summary of Sections 2.5 and 2.6; *2.6e. Redescending M-Estimators for Scale; 2.7. Relation with Huber's Minimax Approach; Exercises and Problems; 3. ONE-DIMENSIONAL TESTS; 3.1. Introduction; 3.2. The Influence Function for Tests; 3.2a. Definition of the Influence Function; 3.2b. Properties of the Influence Function; 3.2c. Relation with Level and Power; 3.2d. Connection with Shift Estimators; 3.3. Classes of Tests; 3.3a The One-Sample Case; 3.3b. The Two-Sample Case; 3.4. Optimally Bounding the Gross-Error Sensitivity 3.5. Extending the Change-of-Variance Function to Tests
Record Nr.	UNINA-9910139564803321