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**Robust statistics.
2nd revised ed.**
*(English)*
Zbl 1276.62022

Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons (ISBN 978-0-470-12990-6/hbk; 978-0-470-43469-7/ebook). xvi, 354 p. (2009).

The book under review is the second edition of P.J. Huber’s monograph of the same title from 1981, see the review Zbl 0536.62025. Even though much of the first edition material is still valid, at least an update of the bibliographical references was required. Moreover, since 1981 there have been new developments with regard to breakdown points, infinitesimal robustness, robust tests, and small sample asymptotics. To reflect these developments, new chapters have been added to this edition. Also, the discussion of regression is extended and a new chapter is added on Bayesian robustness. Some of the general remarks at the beginning of the chapters have been expanded and more space is devoted to an informal discussion of motivation. The cited book consists of 15 chapters and an updated bibliography. Below the list of chapters:

Chapter 1. Generalities.

Chapter 2. The weak topology and its metrization.

Chapter 3. The basic types of estimates.

Chapter 4. Asymptotic minimax theory for estimation location.

Chapter 5. Scale estimators.

Chapter 6. Multiparameter problems in particular joint estimation of location and scale.

Chapter 7. Regression.

Chapter 8. Robust covariance and correlation matrices.

Chapter 9. Robustness of design.

Chapter 10. Exact finite sample results.

Chapter 11. Finite sample breakdown point.

Chapter 12. Infinitesimal robustness.

Chapter 13. Robust tests.

Chapter 14. Small sample asymptotics.

Chapter 15. Bayesian robustness.

Chapter 1. Generalities.

Chapter 2. The weak topology and its metrization.

Chapter 3. The basic types of estimates.

Chapter 4. Asymptotic minimax theory for estimation location.

Chapter 5. Scale estimators.

Chapter 6. Multiparameter problems in particular joint estimation of location and scale.

Chapter 7. Regression.

Chapter 8. Robust covariance and correlation matrices.

Chapter 9. Robustness of design.

Chapter 10. Exact finite sample results.

Chapter 11. Finite sample breakdown point.

Chapter 12. Infinitesimal robustness.

Chapter 13. Robust tests.

Chapter 14. Small sample asymptotics.

Chapter 15. Bayesian robustness.

Reviewer: Joseph Melamed (Los Angeles)