Unmasking Multiple Outliers in Multivariate Data

We proposed a procedure for detecting of multiple outliers in multivariate data. Rousseeuw and van Zomeren (1990) have suggested the robust distance $RD_i$ by using the Resampling Algorithm. But $RD_i$ are based on the assumption that X is in the general position.(X is said to be in the general position when every subsample of size p+1 has rank p) From the practical points of view, this is clearly unrealistic. In this paper, we proposed a computing method for approximating MVE, which is not subject to these problems. The procedure is easy to compute, and works well even if subsample is singular or nearly singular matrix.