A Detection Method of Multivariate Outliers using Decompositions of the Squared Mahalanobis Distance

Kim(2000) proposed two meaningful decompositions of the squared Mahalanobis distance to uncover the sources of outlyingness for multivariate observations. The decompo- sition is useful for identifying some component variables dominating the Mahalanobis distance. In this article we considered the distributions for components of the decompo- sitions and we showed that each component follows a normal distribution and the random vector consisting of two components is a multivariate normal distribution. We may detect outliers using the cut-off values. We proposed a graphical tool for detecting multivariate outliers through one-sheet figure. It is a very useful result to analyze the outlyingness for high dimensional data. Two illustrative examples are given.