Bivariate boxplots, multiple outliers, multivariate transformations and discriminant analysis: The 1997 Hunter Lecture
✍ Scribed by Anthony C. Atkinson; Marco Riani
- Book ID
- 101277730
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 276 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1180-4009
No coin nor oath required. For personal study only.
✦ Synopsis
Outliers can have a large in¯uence on the model ®tted to data. The models we consider are the transformation of data to approximate normality and also discriminant analysis, perhaps on transformed observations. If there are only one or a few outliers, they may often be detected by the deletion methods associated with regression diagnostics. These can be thought of as backwards' methods, as they start from a model ®tted to all the data. However such methods become cumbersome, and may fail, in the presence of multiple outliers. We instead consider a forward' procedure in which very robust methods, such as least median of squares, are used to select a small, outlier free, subset of the data. This subset is increased in size using a search which avoids the inclusion of outliers. During the forward search we monitor quantities of interest, such as score statistics for transformation or, in discriminant analysis, misclassi®cation probabilities. Examples demonstrate how the method very clearly reveals structure in the data and ®nds in¯uential observations, which appear towards the end of the search. In our examples these in¯uential observations can readily be related to patterns in the original data, perhaps after transformation.