The influence function of the Stahel-Donoho covariance estimator of smallest outlyingness

In traditional multivariate location and scatter estimation based on the Stahel-Donoho outlyingness, a weight function is applied, usually calibrated with respect to the multivariate Gaussian distribution. Other robust methods compute the covariance matrix of a fixed size subset of the data (e.g. the MCD estimator). In this paper we study a combination of both the ideas. Location and scatter are estimated using a fixed size subset of the data containing the points with smallest Stahel-Donoho outlyingness. Local robustness and asymptotic relative efficiency are investigated.