ODIF for L-filters

In this paper we study robustness of L-filters by using a recently introduced method called output distributional influence function (ODIF). Unlike the traditionally used methods, such as the influence function and the change-of-variance function, the ODIF provides information about the robustness of finite length filters. So the ODIF is not only a good theoretical analysis tool but it can also be used in real filtering situations for selecting filters behaving as desired in the presence of contamination. The usefulness of the ODIF in the analysis of the robustness of different L-filters is demonstrated in several illustrative examples by using the ODIFs for the expectation and the variance giving local robustness of the value and the variance, respectively.