If a symmetric distribution is ε-contaminated and the contaminants have finite first moments, the median may cease to be the most robust estimator of location.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-1,
author = {Ryszard Zieli\'nski},
title = {The most stable estimator of location under integrable contaminants},
journal = {Applicationes Mathematicae},
volume = {29},
year = {2002},
pages = {1-6},
zbl = {1053.62040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-1}
}
Ryszard Zieliński. The most stable estimator of location under integrable contaminants. Applicationes Mathematicae, Tome 29 (2002) pp. 1-6. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-1/