A note on bias robustness of the median

Zhiqiang Chen

Statistics & Probability Letters, 1998, vol. 38, issue 4, 363-368

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.

Keywords: Bias; robustness; Median; Minimaxity (search for similar items in EconPapers)
Date: 1998
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