摘要：It is known that the robustness properties of estimators depend
on the choice of a metric in the space of distributions. We introduce
a version of Hampel's qualitative robustness that takes into account the -asymptotic normality of estimators in , and examine such
robustness of two standard location estimators in . For this purpose, we use certain combination of the Kantorovich and Zolotarev
metrics rather than the usual Prokhorov type metric. This choice of
the metric is explained by an intention to expose a (theoretical) situation where the robustness properties of sample mean and -sample median are in reverse to the usual ones. Using the mentioned probability
metrics we show the qualitative robustness of the sample multivariate
mean and prove the inequality which provides a quantitative measure
of robustness. On the other hand, we show that -sample median could not be “qualitatively robust” with respect to the same distance
between the distributions.
