Robust Distances: Simulations and Cutoff Values

Abstract

It is possible to detect outliers in multivariate point clouds by computing distances based on robust estimates of location and scale. It has been suggested to use the Minimum Volume Ellipsoid estimator, which can be computed using a resampling algorithm. In this paper the small sample behavior of the robust distances is studied by means of simulation. We obtain a correction factor yielding approximately correct coverage percentages for the corresponding ellipsoids. In addition, a projection-type algorithm is considered to overcome the computational complexity of the resampling algorithm. Advantages and disadvantages of the second algorithm are discussed.