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We provide an asymptotic expansion of the maximal mean squared error (MSE) ofthe sample median to be attained on shrinking gross error neighborhoods aboutan ideal central distribution. More specifically, this expansion comes inpowers of n^{-1/2}, for n the sample size, and uses a shrinking rate ofn^{-1/2} as well. This refines corresponding results of first order asymptoticsto be found in Rieder[94]. In contrast to usual higher order asymptotics, we donot approximate distribution functions (or densities) in the first place, butrather expand the risk directly. Our results are illustrated by comparing themto the results of a simulation study and to numerically evaluated exact MSE'sin both ideal and contaminated situation.

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