A note on bias robustness of the median
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.
Year of publication: |
1998
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Authors: | Chen, Zhiqiang |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 38.1998, 4, p. 363-368
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Publisher: |
Elsevier |
Subject: | Bias robustness Median Minimaxity |
Saved in:
Online Resource
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