A Subsampling Method for the Computation of Multivariate Estimators with High Breakdown Point

Abstract

All known robust location and scale estimators with high breakdown point for multivariate samples are very expensive to compute. In practice, this computation has to be carried out using an approximate subsampling procedure. In this article we describe an alternative subsampling scheme, applicable to both the Stahel-Donoho estimator and the minimum volume ellipsoid estimator, with the property that the number of subsamples required can be substantially reduced with respect to the standard subsampling procedures used in both cases. We also discuss some bias and variability properties of the estimator obtained from the proposed subsampling process.