Though widely accepted, in nonparametric models admitting asymmetric distributions the sample median, if n=2k, may be a poor estimator of the population median. Shortcomings of estimators which are not equivariant are presented.
@article{bwmeta1.element.bwnjournal-article-zmv23i3p363bwm,
author = {Ryszard Zieli\'nski},
title = {Estimating median and other quantiles in nonparametric models},
journal = {Applicationes Mathematicae},
volume = {23},
year = {1995},
pages = {363-370},
zbl = {0836.62028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv23i3p363bwm}
}
Zieliński, Ryszard. Estimating median and other quantiles in nonparametric models. Applicationes Mathematicae, Tome 23 (1995) pp. 363-370. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv23i3p363bwm/
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