Robust Statistics, 2nd Edition

Robust Statistics, 2nd Edition

by Ricardo A. Maronna, R. Douglas Martin, Victor J. Yohai, Matías Salibián-Barrera
Released January 2019
Publisher(s): Wiley
ISBN: 9781119214687

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Book description

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.

Table of contents

  1. Cover
  2. Dedication
  3. Preface
    1. Finite‐sample robustness
    2. Fast and reliable starting points for initial estimators
    3. Robust regularized regression
    4. Multivariate location and scatter estimation with missing data
    5. Robust estimation with independent outliers in variables
    6. Mixed linear models
    7. Generalized linear models
    8. Regularized robust estimators of the inverse covariance matrix
    9. A note on software and book web site
  4. Preface to the First Edition
    1. Why robust statistics are needed
    2. Purpose of the book
    3. Intended audience
    4. Organization of the Book
    5. How to read this book
    6. Computing
    7. S‐PLUS software download
    8. Acknowledgements
    9. Authors' note on publication of the Second Edition
  5. About the Companion Website
  6. 1 Introduction
    1. 1.1 Classical and robust approaches to statistics
    2. 1.2 Mean and standard deviation
    3. 1.3 The “three sigma edit” rule
    4. 1.4 Linear regression
    5. 1.5 Correlation coefficients
    6. 1.6 Other parametric models
    7. 1.7 Problems
  7. 2 Location and Scale
    1. 2.1 The location model
    2. 2.2 Formalizing departures from normality
    3. 2.3 M‐estimators of location
    4. 2.4 Trimmed and Winsorized means
    5. 2.5 M‐estimators of scale
    6. 2.6 Dispersion estimators
    7. 2.7 M‐estimators of location with unknown dispersion
    8. 2.8 Numerical computing of M‐estimators
    9. 2.9 Robust confidence intervals and tests
    10. 2.10 Appendix: proofs and complements
    11. 2.11 Recommendations and software
    12. 2.12 Problems
  8. 3 Measuring Robustness
    1. 3.1 The influence function
    2. 3.2 The breakdown point
    3. 3.3 Maximum asymptotic bias
    4. 3.4 Balancing robustness and efficiency
    5. 3.5 *“Optimal” robustness
    6. 3.6 Multidimensional parameters
    7. 3.7 *Estimators as functionals
    8. 3.8 Appendix: Proofs of results
    9. 3.9 Problems
  9. 4 Linear Regression 1
    1. 4.1 Introduction
    2. 4.2 Review of the least squares method
    3. 4.3 Classical methods for outlier detection
    4. 4.4 Regression M‐estimators
    5. 4.5 Numerical computing of monotone M‐estimators
    6. 4.6 BP of monotone regression estimators
    7. 4.7 Robust tests for linear hypothesis
    8. 4.8 *Regression quantiles
    9. 4.9 Appendix: Proofs and complements
    10. 4.10 Recommendations and software
    11. 4.11 Problems
  10. 5 Linear Regression 2
    1. 5.1 Introduction
    2. 5.2 The linear model with random predictors
    3. 5.3 M‐estimators with a bounded ‐function
    4. 5.4 Estimators based on a robust residual scale
    5. 5.5 MM‐estimators
    6. 5.6 Robust inference and variable selection for M‐estimators
    7. 5.7 Algorithms
    8. 5.8 Balancing asymptotic bias and efficiency
    9. 5.9 Improving the efficiency of robust regression estimators
    10. 5.10 Robust regularized regression
    11. 5.11 *Other estimators
    12. 5.12 Other topics
    13. 5.13 *Appendix: proofs and complements
    14. 5.14 Recommendations and software
    15. 5.15 Problems
  11. 6 Multivariate Analysis
    1. 6.1 Introduction
    2. 6.2 Breakdown and efficiency of multivariate estimators
    3. 6.3 M‐estimators
    4. 6.4 Estimators based on a robust scale
    5. 6.5 MM‐estimators
    6. 6.6 The Stahel–Donoho estimator
    7. 6.7 Asymptotic bias
    8. 6.8 Numerical computing of multivariate estimators
    9. 6.9 Faster robust scatter matrix estimators
    10. 6.10 Choosing a location/scatter estimator
    11. 6.11 Robust principal components
    12. 6.12 Estimation of multivariate scatter and location with missing data
    13. 6.13 Robust estimators under the cellwise contamination model
    14. 6.14 Regularized robust estimators of the inverse of the covariance matrix
    15. 6.15 Mixed linear models
    16. 6.16 *Other estimators of location and scatter
    17. 6.17 Appendix: proofs and complements
    18. 6.18 Recommendations and software
    19. 6.19 Problems
  12. 7 Generalized Linear Models
    1. 7.1 Binary response regression
    2. 7.2 Robust estimators for the logistic model
    3. 7.3 Generalized linear models
    4. 7.4 Transformed M‐estimators
    5. 7.5 Recommendations and software
    6. 7.6 Problems
  13. 8 Time Series
    1. 8.1 Time series outliers and their impact
    2. 8.2 Classical estimators for AR models
    3. 8.3 Classical estimators for ARMA models
    4. 8.4 M‐estimators of ARMA models
    5. 8.5 Generalized M‐estimators
    6. 8.6 Robust AR estimation using robust filters
    7. 8.7 Robust model identification
    8. 8.8 Robust ARMA model estimation using robust filters
    9. 8.9 ARIMA and SARIMA models
    10. 8.10 Detecting time series outliers and level shifts
    11. 8.11 Robustness measures for time series
    12. 8.12 Other approaches for ARMA models
    13. 8.13 High‐efficiency robust location estimators
    14. 8.14 Robust spectral density estimation
    15. 8.15 Appendix A: Heuristic derivation of the asymptotic distribution of M‐estimators for ARMA models
    16. 8.16 Appendix B: Robust filter covariance recursions
    17. 8.17 Appendix C: ARMA model state‐space representation
    18. 8.18 Recommendations and software
    19. 8.19 Problems
  14. 9 Numerical Algorithms
    1. 9.1 Regression M‐estimators
    2. 9.2 Regression S‐estimators
    3. 9.3 The LTS‐estimator
    4. 9.4 Scale M‐estimators
    5. 9.5 Multivariate M‐estimators
    6. 9.6 Multivariate S‐estimators
  15. 10 Asymptotic Theory of M‐estimators
    1. 10.1 Existence and uniqueness of solutions
    2. 10.2 Consistency
    3. 10.3 Asymptotic normality
    4. 10.4 Convergence of the SC to the IF
    5. 10.5 M‐estimators of several parameters
    6. 10.6 Location M‐estimators with preliminary scale
    7. 10.7 Trimmed means
    8. 10.8 Optimality of the MLE
    9. 10.9 Regression M‐estimators: existence and uniqueness
    10. 10.10 Regression M‐estimators: asymptotic normality
    11. 10.11 Regression M estimators: Fisher‐consistency
    12. 10.12 Nonexistence of moments of the sample median
    13. 10.13 Problems
  16. 11 Description of Datasets
    1. Alcohol
    2. Algae
    3. Aptitude
    4. Bus
    5. Glass
    6. Hearing
    7. Image
    8. Krafft
    9. Neuralgia
    10. Oats
    11. Solid waste
    12. Stack loss
    13. Toxicity
    14. Wine
  17. References
  18. Index
  19. End User License Agreement

Product information

  • Title: Robust Statistics, 2nd Edition
  • Author(s): Ricardo A. Maronna, R. Douglas Martin, Victor J. Yohai, Matías Salibián-Barrera
  • Release date: January 2019
  • Publisher(s): Wiley
  • ISBN: 9781119214687