Stahel–Donoho estimation for high-dimensional data

Abstract

We discuss two recently proposed adaptations of the well-known Stahel–Donoho estimator of multivariate location and scatter for high-dimensional data. The first adaptation adjusts the calculation of the outlyingness of the observations while the second adaptation allows to give separate weights to each of the components of an observation. Both adaptations address the possibility that in higher dimensions most observations can be contaminated in at least one of its components. We then combine the two approaches in a new method and investigate its performance in comparison to the previously proposed methods.

Keywords:

• high-dimensional data
• robustness
• location and scatter estimation
• outlyingness
• cellwise weights

2010 AMS Subject Classifications:

• 62F35
• 62H12

Acknowledgements

This work was supported by a grant of the Fund for Scientific Research-Flanders [grant number G.0.077.11.N.10] and by Interuniversity Attraction Pole (IAP) research network grant of the Belgian government (Belgian Science Policy) [grant number P7/06].