New Algorithms for $M$-Estimation of Multivariate Location and Scatter

Lutz Duembgen, Klaus Nordhausen, Heike Schuhmacher

Published 2013-12-23, updated 2015-05-20Version 4

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 related algorithms. The main idea is to utilize a second order Taylor expansion 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.