Muutke küpsiste eelistusi

E-raamat: Robust Statistics - Theory and Methods (with R) Second Edition: Theory and Methods (with R) 2nd Edition [Wiley Online]

(The University of British Columbia), (Universidad Nacional de La Plata, Argentina), (University of Buenos Aires, Argentina), (University of Washington, USA)
Teised raamatud teemal:
  • Wiley Online
  • Hind: 100,44 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Robust Statistics - Theory and Methods (with R) Second Edition: Theory and Methods (with R) 2nd EditionSuurem pilt
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119214656

A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R.

Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book.

Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates.

  • Explains both the use and theoretical justification of robust methods
  • Guides readers in selecting and using the most appropriate robust methods for their problems
  • Features computational algorithms for the core methods

Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models.

Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

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(16)
1.1 Classical and robust approaches to statistics
1(1)
1.2 Mean and standard deviation
2(4)
1.3 The "three sigma edit" rule
6(2)
1.4 Linear regression
8(4)
1.4.1 Straight-line regression
8(1)
1.4.2 Multiple linear regression
9(3)
1.5 Correlation coefficients
12(1)
1.6 Other parametric models
13(3)
1.7 Problems
16(1)
2 Location and Scale 17(34)
2.1 The location model
17(2)
2.2 Formalizing departures from normality
19(3)
2.3 M-estimators of location
22(9)
2.3.1 Generalizing maximum likelihood
22(3)
2.3.2 The distribution of M-estimators
25(3)
2.3.3 An intuitive view of M-estimators
28(1)
2.3.4 Redescending M-estimators
29(2)
2.4 Trimmed and Winsorized means
31(2)
2.5 M-estimators of scale
33(2)
2.6 Dispersion estimators
35(2)
2.7 M-estimators of location with unknown dispersion
37(3)
2.7.1 Previous estimation of dispersion
38(1)
2.7.2 Simultaneous M-estimators of location and dispersion
38(2)
2.8 Numerical computing of M-estimators
40(2)
2.8.1 Location with previously-computed dispersion estimation
40(1)
2.8.2 Scale estimators
41(1)
2.8.3 Simultaneous estimation of location and dispersion
42(1)
2.9 Robust confidence intervals and tests
42(3)
2.9.1 Confidence intervals
42(2)
2.9.2 Tests
44(1)
2.10 Appendix: proofs and complements
45(3)
2.10.1 Mixtures
45(1)
2.10.2 Asymptotic normality of M-estimators
46(1)
2.10.3 Slutsky's lemma
47(1)
2.10.4 Quantiles
47(1)
2.10.5 Alternative algorithms for M-estimators
47(1)
2.11 Recommendations and software
48(1)
2.12 Problems
49(2)
3 Measuring Robustness 51(36)
3.1 The influence function
55(3)
3.1.1 *The convergence of the SC to the IF
57(1)
3.2 The breakdown point
58(4)
3.2.1 Location M-estimators
59(1)
3.2.2 Scale and dispersion estimators
59(1)
3.2.3 Location with previously-computed dispersion estimator
60(1)
3.2.4 Simultaneous estimation
61(1)
3.2.5 Finite-sample breakdown point
61(1)
3.3 Maximum asymptotic bias
62(2)
3.4 Balancing robustness and efficiency
64(2)
3.5 *"Optimal" robustness
66(4)
3.5.1 Bias-and variance-optimality of location estimators
66(1)
3.5.2 Bias optimality of scale and dispersion estimators
66(1)
3.5.3 The infinitesimal approach
67(1)
3.5.4 The Hampel approach
68(2)
3.5.5 Balancing bias and variance: the general problem
70(1)
3.6 Multidimensional parameters
70(2)
3.7 *Estimators as functionals
72(4)
3.8 Appendix: Proofs of results
76(9)
3.8.1 IF of general M-estimators
76(1)
3.8.2 Maximum BP of location estimators
76(1)
3.8.3 BP of location M-estimators
77(2)
3.8.4 Maximum bias of location M-estimators
79(1)
3.8.5 The minimax bias property of the median
80(1)
3.8.6 Minimizing the GES
80(2)
3.8.7 Hampel optimality
82(3)
3.9 Problems
85(2)
4 Linear Regression 1 87(28)
4.1 Introduction
87(4)
4.2 Review of the least squares method
91(3)
4.3 Classical methods for outlier detection
94(3)
4.4 Regression M-estimators
97(6)
4.4.1 M-estimators with known scale
99(1)
4.4.2 M-estimators with preliminary scale
100(2)
4.4.3 Simultaneous estimation of regression and scale
102(1)
4.5 Numerical computing of monotone M-estimators
103(1)
4.5.1 The L1 estimator
103(1)
4.5.2 M-estimators with smooth ψ-function
104(1)
4.6 BP of monotone regression estimators
104(2)
4.7 Robust tests for linear hypothesis
106(3)
4.7.1 Review of the classical theory
106(2)
4.7.2 Robust tests using M-estimators
108(1)
4.8 *Regression quantiles
109(1)
4.9 Appendix: Proofs and complements
110(3)
4.9.1 Why equivariance?
110(1)
4.9.2 Consistency of estimated slopes under asymmetric errors
110(1)
4.9.3 Maximum FBP of equivariant estimators
111(1)
4.9.4 The FBP of monotone M-estimators
112(1)
4.10 Recommendations and software
113(1)
4.11 Problems
113(2)
5 Linear Regression 2 115(80)
5.1 Introduction
115(3)
5.2 The linear model with random predictors
118(1)
5.3 M-estimators with a bounded ρ-function
119(5)
5.3.1 Properties of M-estimators with a bounded ρ-function
120(4)
5.4 Estimators based on a robust residual scale
124(4)
5.4.1 S-estimators
124(2)
5.4.2 L-estimators of scale and the LTS estimator
126(1)
5.4.3 τ-estimators
127(1)
5.5 MM-estimators
128(5)
5.6 Robust inference and variable selection for M-estimators
133(5)
5.6.1 Bootstrap robust confidence intervals and tests
134(1)
5.6.2 Variable selection
135(3)
5.7 Algorithms
138(12)
5.7.1 Finding local minima
140(1)
5.7.2 Starting values: the subsampling algorithm
141(2)
5.7.3 A strategy for faster subsampling-based algorithms
143(1)
5.7.4 Starting values: the Pena-Yohai estimator
144(2)
5.7.5 Starting values with numeric and categorical predictors
146(3)
5.7.6 Comparing initial estimators
149(1)
5.8 Balancing asymptotic bias and efficiency
150(5)
5.8.1 "Optimal" redescending M-estimators
153(2)
5.9 Improving the efficiency of robust regression estimators
155(9)
5.9.1 Improving efficiency with one-step reweighting
155(1)
5.9.2 A fully asymptotically efficient one-step procedure
156(2)
5.9.3 Improving finite-sample efficiency and robustness
158(6)
5.9.4 Choosing a regression estimator
164(1)
5.10 Robust regularized regression
164(8)
5.10.1 Ridge regression
165(3)
5.10.2 Lasso regression
168(3)
5.10.3 Other regularized estimators
171(1)
5.11 *Other estimators
172(4)
5.11.1 Generalized M-estimators
172(2)
5.11.2 Projection estimators
174(1)
5.11.3 Constrained M-estimators
175(1)
5.11.4 Maximum depth estimators
175(1)
5.12 Other topics
176(6)
5.12.1 The exact fit property
176(1)
5.12.2 Heteroskedastic errors
177(3)
5.12.3 A robust multiple correlation coefficient
180(2)
5.13 *Appendix: proofs and complements
182(9)
5.13.1 The BP of monotone M-estimators with random X
182(1)
5.13.2 Heavy-tailed x
183(1)
5.13.3 Proof of the exact fit property
183(1)
5.13.4 The BP of S-estimators
184(2)
5.13.5 Asymptotic bias of M-estimators
186(1)
5.13.6 Hampel optimality for GM-estimators
187(1)
5.13.7 Justification of RFPE*
188(3)
5.14 Recommendations and software
191(1)
5.15 Problems
191(4)
6 Multivariate Analysis 195(76)
6.1 Introduction
195(5)
6.2 Breakdown and efficiency of multivariate estimators
200(2)
6.2.1 Breakdown point
200(1)
6.2.2 The multivariate exact fit property
201(1)
6.2.3 Efficiency
201(1)
6.3 M-estimators
202(5)
6.3.1 Collinearity
205(1)
6.3.2 Size and shape
205(1)
6.3.3 Breakdown point
206(1)
6.4 Estimators based on a robust scale
207(8)
6.4.1 The minimum volume ellipsoid estimator
208(1)
6.4.2 S-estimators
208(2)
6.4.3 The MCD estimator
210(1)
6.4.4 S-estimators for high dimension
210(4)
6.4.5 τ-estimators
214(1)
6.4.6 One-step reweighting
215(1)
6.5 MM-estimators
215(2)
6.6 The Stahel-Donoho estimator
217(2)
6.7 Asymptotic bias
219(1)
6.8 Numerical computing of multivariate estimators
220(4)
6.8.1 Monotone M-estimators
220(1)
6.8.2 Local solutions for S-estimators
221(1)
6.8.3 Subsampling for estimators based on a robust scale
221(2)
6.8.4 The MVE
223(1)
6.8.5 Computation of S-estimators
223(1)
6.8.6 The MCD
223(1)
6.8.7 The Stahel-Donoho estimator
224(1)
6.9 Faster robust scatter matrix estimators
224(5)
6.9.1 Using pairwise robust covariances
224(4)
6.9.2 The Pena-Prieto procedure
228(1)
6.10 Choosing a location/scatter estimator
229(5)
6.10.1 Efficiency
230(1)
6.10.2 Behavior under contamination
231(1)
6.10.3 Computing times
232(1)
6.10.4 Tuning constants
233(1)
6.10.5 Conclusions
233(1)
6.11 Robust principal components
234(6)
6.11.1 Spherical principal components
236(1)
6.11.2 Robust PCA based on a robust scale
237(3)
6.12 Estimation of multivariate scatter and location with missing data
240(2)
6.12.1 Notation
240(1)
6.12.2 GS estimators for missing data
241(1)
6.13 Robust estimators under the cellwise contamination model
242(3)
6.14 Regularized robust estimators of the inverse of the covariance matrix
245(1)
6.15 Mixed linear models
246(8)
6.15.1 Robust estimation for MLM
248(1)
6.15.2 Breakdown point of MLM estimators
248(2)
6.15.3 S-estimators for MLMs
250(1)
6.15.4 Composite τ-estimators
250(4)
6.16 *Other estimators of location and scatter
254(2)
6.16.1 Projection estimators
254(1)
6.16.2 Constrained M-estimators
255(1)
6.16.3 Multivariate depth
256(1)
6.17 Appendix: proofs and complements
256(12)
6.17.1 Why affine equivariance?
256(1)
6.17.2 Consistency of equivariant estimators
256(1)
6.17.3 The estimating equations of the MLE
257(1)
6.17.4 Asymptotic BP of monotone M-estimators
258(2)
6.17.5 The estimating equations for S-estimators
260(1)
6.17.6 Behavior of S-estimators for high p
261(1)
6.17.7 Calculating the asymptotic covariance matrix of location M-estimators
262(1)
6.17.8 The exact fit property
263(1)
6.17.9 Elliptical distributions
264(1)
6.17.10 Consistency of Gnanadesikan-Kettenring correlations
265(1)
6.17.11 Spherical principal components
266(1)
6.17.12 Fixed point estimating equations and computing algorithm for the GS estimator
267(1)
6.18 Recommendations and software
268(1)
6.19 Problems
269(2)
7 Generalized Linear Models 271(22)
7.1 Binary response regression
271(4)
7.2 Robust estimators for the logistic model
275(6)
7.2.1 Weighted MLEs
275(1)
7.2.2 Redescending M-estimators
276(5)
7.3 Generalized linear models
281(3)
7.3.1 Conditionally unbiased bounded influence estimators
283(1)
7.4 Transformed M-estimators
284(5)
7.4.1 Definition of transformed M-estimators
284(2)
7.4.2 Some examples of variance-stabilizing transformations
286(1)
7.4.3 Other estimators for GLMs
286(3)
7.5 Recommendations and software
289(1)
7.6 Problems
290(3)
8 Time Series 293(70)
8.1 Time series outliers and their impact
294(8)
8.1.1 Simple examples of outliers influence
296(2)
8.1.2 Probability models for time series outliers
298(3)
8.1.3 Bias impact of AOs
301(1)
8.2 Classical estimators for AR models
302(6)
8.2.1 The Durbin-Levinson algorithm
305(2)
8.2.2 Asymptotic distribution of classical estimators
307(1)
8.3 Classical estimators for ARMA models
308(2)
8.4 M-estimators of ARMA models
310(3)
8.4.1 M-estimators and their asymptotic distribution
310(1)
8.4.2 The behavior of M-estimators in AR processes with additive outliers
311(1)
8.4.3 The behavior of LS and M-estimators for ARMA processes with infinite innovation variance
312(1)
8.5 Generalized M-estimators
313(2)
8.6 Robust AR estimation using robust filters
315(6)
8.6.1 Naive minimum robust scale autoregression estimators
315(1)
8.6.2 The robust filter algorithm
316(2)
8.6.3 Minimum robust scale estimators based on robust filtering
318(1)
8.6.4 A robust Durbin-Levinson algorithm
319(1)
8.6.5 Choice of scale for the robust Durbin-Levinson procedure
320(1)
8.6.6 Robust identification of AR order
320(1)
8.7 Robust model identification
321(3)
8.8 Robust ARMA model estimation using robust filters
324(5)
8.8.1 τ-estimators of ARMA models
324(2)
8.8.2 Robust filters for ARMA models
326(2)
8.8.3 Robustly filtered τ-estimators
328(1)
8.9 ARIMA and SARIMA models
329(4)
8.10 Detecting time series outliers and level shifts
333(7)
8.10.1 Classical detection of time series outliers and level shifts
334(2)
8.10.2 Robust detection of outliers and level shifts for ARIMA models
336(2)
8.10.3 REGARIMA models: estimation and outlier detection
338(2)
8.11 Robustness measures for time series
340(5)
8.11.1 Influence function
340(2)
8.11.2 Maximum bias
342(1)
8.11.3 Breakdown point
343(1)
8.11.4 Maximum bias curves for the AR(1) model
343(2)
8.12 Other approaches for ARMA models
345(2)
8.12.1 Estimators based on robust autocovariances
345(1)
8.12.2 Estimators based on memory-m prediction residuals
346(1)
8.13 High-efficiency robust location estimators
347(1)
8.14 Robust spectral density estimation
348(8)
8.14.1 Definition of the spectral density
348(1)
8.14.2 AR spectral density
349(1)
8.14.3 Classic spectral density estimation methods
349(1)
8.14.4 Prewhitening
350(1)
8.14.5 Influence of outliers on spectral density estimators
351(2)
8.14.6 Robust spectral density estimation
353(1)
8.14.7 Robust time-average spectral density estimator
354(2)
8.15 Appendix A: Heuristic derivation of the asymptotic distribution of M-estimators for ARMA models
356(3)
8.16 Appendix B: Robust filter covariance recursions
359(1)
8.17 Appendix C: ARMA model state-space representation
360(1)
8.18 Recommendations and software
361(1)
8.19 Problems
361(2)
9 Numerical Algorithms 363(10)
9.1 Regression M-estimators
363(3)
9.2 Regression S-estimators
366(1)
9.3 The LTS-estimator
366(1)
9.4 Scale M-estimators
367(2)
9.4.1 Convergence of the fixed-point algorithm
367(1)
9.4.2 Algorithms for the non-concave case
368(1)
9.5 Multivariate M-estimators
369(1)
9.6 Multivariate S-estimators
370(3)
9.6.1 S-estimators with monotone weights
370(1)
9.6.2 The MCD
371(1)
9.6.3 S-estimators with non-monotone weights
371(1)
9.6.4 *Proof of (9.27)
372(1)
10 Asymptotic Theory of M-estimators 373(28)
10.1 Existence and uniqueness of solutions
374(2)
10.1.1 Redescending location estimators
375(1)
10.2 Consistency
376(1)
10.3 Asymptotic normality
377(2)
10.4 Convergence of the SC to the IF
379(2)
10.5 M-estimators of several parameters
381(3)
10.6 Location M-estimators with preliminary scale
384(2)
10.7 Trimmed means
386(1)
10.8 Optimality of the MLE
386(2)
10.9 Regression M-estimators: existence and uniqueness
388(1)
10.10 Regression M-estimators: asymptotic normality
389(5)
10.10.1 Fixed X
389(5)
10.10.2 Asymptotic normality: random X
394(1)
10.11 Regression M estimators: Fisher-consistency
394(4)
10.11.1 Redescending estimators
394(2)
10.11.2 Monotone estimators
396(2)
10.12 Nonexistence of moments of the sample median
398(1)
10.13 Problems
399(2)
11 Description of Datasets 401(6)
References 407(16)
Index 423
Ricardo A. Maronna, Consultant Professor, National University of La Plata, Argentina

R. Douglas Martin, Departments of Applied Mathematics and Statistics, University of Washington, USA

Victor J. Yohai, Department of Mathematics, University of Buenos Aires, and CONICET, Argentina

Matías Salibián-Barrera, Department of Statistics, The University of British Columbia, Canada
Püsilink: https://www.kriso.ee/db/9781119214656_pe.html
Märksõnad: