Interactions and outliers in the two-way analysis of variance

• 成果类型: Article
• 署名作者: Terbeck, W; Davies, PL
• 署名单位: University of Duisburg Essen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1279-1305
• 关键词: regression; breakdown

摘要

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 shown that the standard definition of interactions is counterintuitive and obfuscates rather than clarifies. A different definition of interaction is given which among 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 call be identified by the L-1 functional. The unconditionally identifiable interaction patterns describe the optimal breakdown behavior of any equivariant location functional from which it follows that the L-1 functional has optimal breakdown behavior. 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 al,plied to some data sets including one describing the results of an interlaboratory test.