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**The identification of multiple outliers. (With comments).**
*(English)*
Zbl 0797.62025

A definition of outliers is given in terms of their position relative to the model for good observations. The outlier identification problem is then the problem of identifying those observations that lie in a so- called outlier region. Performance of outlier identifiers is discussed. Besides, breakdown points of some outlier identification procedures are studied in details.

Methods based on robust statistics and outward testing are shown to have the highest possible breakdown points. A detailed analysis shows that methods based on robust statistics perform better with respect to worst- case behavior. An outlier identifier based on a suggestion of Hampel is given. The asymptotic results are augmented by simulations for small sample sizes.

There are comments on the paper given by Nick Fieller, Vic Barnett and A. H. Welsh, and also a reply to the comments by the authors.

Methods based on robust statistics and outward testing are shown to have the highest possible breakdown points. A detailed analysis shows that methods based on robust statistics perform better with respect to worst- case behavior. An outlier identifier based on a suggestion of Hampel is given. The asymptotic results are augmented by simulations for small sample sizes.

There are comments on the paper given by Nick Fieller, Vic Barnett and A. H. Welsh, and also a reply to the comments by the authors.

Reviewer: Y.Wu (North York)

### MSC:

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