Abstract
In this article, it is proved that the median is a minimax bias functional (with respect to many distances including the Kolmogorov distance) among all location equivariant functionals if the distribution of interest is symmetric and unimodal. This is a parallel result of Huber's well-known result (1964). We also proved that the median is no longer a minimax bias functional with respect to several definitions of bias including the contamination bias if the symmetry assumption is violated.
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