The depth of multivariate data can be used to construct weighted means as robust estimators of location. The use of projection depth leads to the Stahel-Donoho estimator as a special case. In contrast to maximal depth estimators, the depth-weighted means are shown to be asymptotically normal under appropriate conditions met by depth functions commonly used in the current literature. We also confirm through a finite-sample study that the Stahel-Donoho estimator achieves a desirable balance between robustness and efficiency at Gaussian models.
"On the Stahel-Donoho estimator and depth-weighted means of multivariate data." Ann. Statist. 32 (1) 167 - 188, February 2004. https://doi.org/10.1214/aos/1079120132