We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in the contamination neighborhood of a continuous distribution. We also define some measures of robustness and efficiency under contamination for confidence intervals and tests. These measures are computed for the proposed procedures.
@article{1098883774,
author = {Yohai, V\'\i ctor J. and Zamar, Ruben H.},
title = {Robust nonparametric inference for the median},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 1841-1857},
language = {en},
url = {http://dml.mathdoc.fr/item/1098883774}
}
Yohai, Víctor J.; Zamar, Ruben H. Robust nonparametric inference for the median. Ann. Statist., Tome 32 (2004) no. 1, pp. 1841-1857. http://gdmltest.u-ga.fr/item/1098883774/