A note on finite sample breakdown points of projection based multivariate location and scatter statistics

Abstract.

In this note, general results of finite sample breakdown point are obtained for two classes of projection based location and scatter statistics: the Stahel-Donoho statistics and the Maronna-Yohai statistics. It is shown that these projection based location and scatter statistics can achieve the maximum breakdown point of affine equivariant multivariate location and scatter statistics. General relationships between the finite sample breakdown point of these statistics and the uniform finite sample breakdown point of the sample median and a modified sample median absolute deviation are formally established.