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**Outliers in statistical data.
3rd ed.**
*(English)*
Zbl 0801.62001

Chichester: John Wiley & Sons, Inc.. xvii, 584 p. (1994).

The third edition of this well known and popular monograph brings up not only revised and updated material covered in the previous editions (for the first, 1978-edition see Zbl 0377.62001, and for the second, 1984- edition Zbl 0638.62002) but much more. Because the book itself is well known among the statistical community, I will concentrate especially on topics in which the coverage is new or has been substantially changed or extended. They include:

Basic principles: distribution theory under contamination models, measures of efficiency and performance for multiple outliers, assessment of masking and swamping, allocation of outliers.

Univariate data: new tests (including extreme and Weibull), wider study of robustness and accommodation (including logistic and double exponential distributions), additional tables.

Multivariate and structural data: estimation of individual components of vector parameters, use of correlation estimators, deletion methods, elliptically symmetric distributions, graphical methods, least median of squares and \(L_ 1\)-norm methods, multivariate linear model, multiple outliers, nonlinear regression (including logistic and generalized linear models).

Special topics: Bayesian methods, time series (ARIMA model, distinction of AO and IO outliers, model specification, new accommodation methods, diagnostics, multiple time series), directional data (methods for axial and vectorial spherical data, accommodation).

Further topics which are dealt with in new chapters include new methods for outliers in contingency tables, problems of sample surveys, statistical software and international standards and regulations. Practical illustrations remain important for reinforcement of ideas – new examples are included as also is discussion of data studies in the literature. Aside that, the References and Bibliography sections have been substantially expanded to cover the new material.

Contents:

Part I. Basic principles.

1. Introduction. 2. Why do outlying observations arise and what should one do about them. 3. The accommodation approach: robust estimation and testing. 4. Testing for discordancy: principles and criteria.

Part II. Univariate data.

5. Accommodation procedures for univariate samples. 6. Specific discordancy tests for outliers in univariate samples.

Part III. Univariate data.

7. Outliers in multivariate data. 8. The outlier problem for structured data: regression, the linear model and design of experiments.

Part IV. Special topics.

9. Bayesian approaches to outliers. 10. Outliers in time series: an important area of outlier study. 11. Outliers in directional data. 12. Some little-explored areas: contingency tables and sample surveys. 13. Important strands: computer software, data studies, standards and regulations.

Basic principles: distribution theory under contamination models, measures of efficiency and performance for multiple outliers, assessment of masking and swamping, allocation of outliers.

Univariate data: new tests (including extreme and Weibull), wider study of robustness and accommodation (including logistic and double exponential distributions), additional tables.

Multivariate and structural data: estimation of individual components of vector parameters, use of correlation estimators, deletion methods, elliptically symmetric distributions, graphical methods, least median of squares and \(L_ 1\)-norm methods, multivariate linear model, multiple outliers, nonlinear regression (including logistic and generalized linear models).

Special topics: Bayesian methods, time series (ARIMA model, distinction of AO and IO outliers, model specification, new accommodation methods, diagnostics, multiple time series), directional data (methods for axial and vectorial spherical data, accommodation).

Further topics which are dealt with in new chapters include new methods for outliers in contingency tables, problems of sample surveys, statistical software and international standards and regulations. Practical illustrations remain important for reinforcement of ideas – new examples are included as also is discussion of data studies in the literature. Aside that, the References and Bibliography sections have been substantially expanded to cover the new material.

Contents:

Part I. Basic principles.

1. Introduction. 2. Why do outlying observations arise and what should one do about them. 3. The accommodation approach: robust estimation and testing. 4. Testing for discordancy: principles and criteria.

Part II. Univariate data.

5. Accommodation procedures for univariate samples. 6. Specific discordancy tests for outliers in univariate samples.

Part III. Univariate data.

7. Outliers in multivariate data. 8. The outlier problem for structured data: regression, the linear model and design of experiments.

Part IV. Special topics.

9. Bayesian approaches to outliers. 10. Outliers in time series: an important area of outlier study. 11. Outliers in directional data. 12. Some little-explored areas: contingency tables and sample surveys. 13. Important strands: computer software, data studies, standards and regulations.

Reviewer: J.Antoch (Praha)

### MSC:

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

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

62F03 | Parametric hypothesis testing |

62F10 | Point estimation |