Robust statistics: Theory and methods.

*(English)*Zbl 1094.62040
Wiley Series in Probability and Statistics. Chichester: John Wiley & Sons (ISBN 0-470-01092-4/hbk; 0-470-01094-0/ebook). xx, 403 p. (2006).

The main motivation of the book is to stimulate use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modeling and data analysis. The book aims at enabling the reader to select and use the most adequate robust methods for various statistical models such as location, scale, linear regression, multivariate statistics, time series and others. For such models exist usually many robust methods (moreover each with several variants) which a data analyst must choose from. In addition to the choice of the most adequate robust method the analyst should understand the theory behind the method. Therefore the book provides for each treated model (1) conceptual and statistical theory explanations, (2) the leading methods proposed so far, (3) comparison of properties of the methods, (4)computational algorithms including S-Plus implementation of different approaches, (5) recommendation of preferred robust methods based on deep experience of the authors that are well-known “robust” statisticians (such a recommendation is a trade-off between estimation theoretical justification and performance, transparency to users and computational costs).

The contents of the book are as follows: Chapter 1 (Introduction) is a data-oriented motivation chapter. Chapter 2 (Location and Scale) deal with methods in the context of location and scale estimation. Chapter 3 (Measuring Robustness) discusses methods for evaluation of the robustness of parameter estimates including optimal estimates based on robustness criteria. Chapters 4 and 5 (Linear Regression 1 and 2) deal with various robust regression methods. Chapter 6 (Multivariate Analysis) treats robust estimation of multivariate location and dispersion and robust principal components. Chapter 7 (Generalized Linear Models) deals, e.g., with logistic regression. Chapter 8 (Time Series) deals with robust estimation of time series models (mainly AR and ARIMA). Chapter 9 (Numerical Algorithms) contains a more detailed treatment of the iterative algorithms for numerical computation of M-estimates. Chapter 10 (Asymptotic Theory of M-estimates) develops the asymptotic theory of some robust procedures. Chapter 11 (Robust Methods in S-Plus) contains instructions on the use of robust procedures written in S-Plus. Chapter 12 describes the data sets used in the book.

The contents of the book are as follows: Chapter 1 (Introduction) is a data-oriented motivation chapter. Chapter 2 (Location and Scale) deal with methods in the context of location and scale estimation. Chapter 3 (Measuring Robustness) discusses methods for evaluation of the robustness of parameter estimates including optimal estimates based on robustness criteria. Chapters 4 and 5 (Linear Regression 1 and 2) deal with various robust regression methods. Chapter 6 (Multivariate Analysis) treats robust estimation of multivariate location and dispersion and robust principal components. Chapter 7 (Generalized Linear Models) deals, e.g., with logistic regression. Chapter 8 (Time Series) deals with robust estimation of time series models (mainly AR and ARIMA). Chapter 9 (Numerical Algorithms) contains a more detailed treatment of the iterative algorithms for numerical computation of M-estimates. Chapter 10 (Asymptotic Theory of M-estimates) develops the asymptotic theory of some robust procedures. Chapter 11 (Robust Methods in S-Plus) contains instructions on the use of robust procedures written in S-Plus. Chapter 12 describes the data sets used in the book.

Reviewer: Tomáš Cipra (Praha)

##### MSC:

62F35 | Robustness and adaptive procedures (parametric inference) |

62G35 | Nonparametric robustness |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

65C60 | Computational problems in statistics (MSC2010) |

62J05 | Linear regression; mixed models |

62H12 | Estimation in multivariate analysis |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |