The DetS and DetMM estimators for multivariate location and scatter

Abstract

New deterministic robust estimators of multivariate location and scatter are presented. They combine ideas from the deterministic DetMCD estimator with steps from the subsampling-based FastS and FastMM algorithms. The new DetS and DetMM estimators perform similarly to FastS and FastMM on low-dimensional data, whereas in high dimensions they are more robust. Their computation time is much lower than FastS and FastMM, which allows to compute the estimators for a range of breakdown values. Moreover, they are permutation invariant and very close to affine equivariant.