Qualitative robustness of von Mises statistics based on strongly mixing data

In this article, the property of qualitative robustness is studied for von Mises statistics in the situation where the observations are not necessarily independent but are drawn from a strongly mixing sequence of identically distributed random variables. The notion of qualitative robustness is taken from “Zähle (2012, submitted)” where Huber’s version of Hampel’s original definition was adapted to the case of dependent observations. The main result is illustrated by means of several examples including the sample variance, the sample Gini’s mean difference and the Cramér–von Mises statistic.