Impartial trimmed means for functional data

In this paper we extend the notion of impartial trimming to a functional data framework, and we obtain resistant estimates of the center of a functional distribution. We give mild conditions for the existence and uniqueness of the functional trimmed means. We show the continuity of the population parameter with respect to the weak convergence of probability measures. As a consequence we obtain consistency and qualitative resistance of the data based estimates. A simplified approximate computational method is also given. Some real data examples are finally analyzed.