## Interactions and Outliers in the Two-Way Analysis of Variance (1998)

Venue: | Annals of Statistics |

Citations: | 5 - 2 self |

### BibTeX

@ARTICLE{Terbeck98interactionsand,

author = {W. Terbeck and P. L. Davies},

title = {Interactions and Outliers in the Two-Way Analysis of Variance},

journal = {Annals of Statistics},

year = {1998},

volume = {26},

pages = {1279--1305}

}

### OpenURL

### Abstract

. The two-way analysis of variance with interactions is a well established and integral part of statistics. In spite of its long standing it is hown that the standard definition of interactions is counter intuitive and obfuscates rather than clarifies. A different definition of interaction is given which amongst other advantages allows the detection of interactions even in the case of one observation per cell. A characterization of unconditionally identifiable interaction patterns is given and it is proved that such patterns can be identified by the L 1 -functional. The unconditionally identifiable interaction patterns describe the optimal breakdown behaviour of any equivariant location functional from which it follows that the L 1 -functional has optimal breakdown behaviour. Possible lack of uniqueness of the L 1 -functional can be overcome using an M-functional with an external scale derived independently from the observations. The resulting procedures are applied to some data ...