A local influence approach to identifying multiple multivariate outliers

We make use of Cook's local influence approach and its recent modification by Poon and Poon to develop measures for detecting multivariate outliers. The motivation and the foundation of the theory are geometrical and are different from classical approaches; however, whilst the proposed measure exhibits a form similar to those in the literature, it still has a considerable advantage in having transformed the classical measures to the unit interval. The new approach unifies outlier identification measures using geometrical concepts. It involves no distributional assumption or large-sample properties, and allows the flexibility of identifying outliers with respect to different metrics. The approach therefore provides a valid reason for using the various measures in complicated situations, such as in non-normal cases and in small-sample problems.