Robust and efficient estimation of multivariate scatter and location

RICARDO A. MARONNA; VÍCTOR J. YOHAI

COMPUTATIONAL STATISTICS AND DATA ANALYSIS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2017 vol. 109 p. 64 - 75

0167-9473

Four families of estimators with controllable eciencies whose performance for moderate to large p has not been explored to date are studied: S-estimators with a non-monotonic weight function, MM-estimators, tau-estimators, and the Stahel-Donoho estimator. Two types of starting estimators are employed: the MVE computed through subsampling, and a semideterministic procedure previously proposed for outlier detection, based on the projections with maximum and minimum kurtosis. A simulation study shows that an S-estimator with non-monotonic weight function can simultaneouslyattain high eciency and high robustness for p 15, while an MM-estimator with a particular weight function can be recommended for p < 15. For both recommended estimators, the initial values are given by the semi-deterministic procedure mentioned above.