The Vasershtein distance as the stability criterion in robust estimation (Corresp.)

In the models used by Hampel as well as by Gray and the author for the qualitative analysis of robust parameter estimators, the Prohorov stability criterion was used. The Vasershtein distance is proposed here as an alternative stability measure. This measure, in contrast to the Prohorov criterion, implies performance stability of the estimators and leads to a constructive analysis for exponentially fast convergence.