Finite-sample replacement breakdown points are derived for different types of estimators of multivariate location and covariance matrices. The role of various equivariance properties is illustrated. The breakdown point is related to a measure of performance based on large deviations probabilities. Finally, we show that one-step reweighting preserves the breakdown point.
"Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices." Ann. Statist. 19 (1) 229 - 248, March, 1991. https://doi.org/10.1214/aos/1176347978