We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and other algorithms. The main idea is to utilize a Taylor expansion of second order of the target functional and devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.
Dümbgen, L., Nordhausen, K., & Schuhmacher, H. (2016). New algorithms for M-estimation of multivariate scatter and location. Journal of Multivariate Analysis, 144, 200–217. https://doi.org/10.1016/j.jmva.2015.11.009