Detecting outliers and influential points: an indirect classical Mahalanobis distance-based method

摘要

In this paper, we consider the problem of detecting outliers and influential points and propose an indirect classical Mahalanobis distance-based method (ICMD) for multivariate datasets. Rousseeuw and Van Zomeren described outliers as those points that do not follow the pattern of the majority of the data; this description has been commonly accepted in the statistical literature. First, we update this description to build ICMD by integrating the following idea: the role of at least one point in the data-driven pattern will be affected greatly before and after excluding an outlier. Then, a similar idea is used to identify influential points. The resulting algorithms are given in detail. Two artificial datasets and three real datasets are applied to show that ICMD is robust, swamping-free, and masking-resistant.