Higher order asymptotics for the MSE of the median on shrinking neighborhoods

Infinitesimal robustness employs first order asymptotics to derive results on uniform (weak) convergence on shrinking neighborhoods around an ideal central model. In the case of the median in the one–dimensional location setup, we refine such a result concerning the convergence of the MSE, proceeding to higher order asymptotics — up to order 1/n , for sample size n . In contrast to usual higher order asymptotics, instead of giving approximations to distribution functions (or densities), we expand the risk directly. These results are illustrated by comparing them to the results of a simulation study and to numerically evaluated exact MSE’s in both ideal and contaminated situation.