Robust nonparametric inference for the median
Abstract
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.
Cite
@article{arxiv.math/0503665,
title = {Robust nonparametric inference for the median},
author = {Victor J. Yohai and Ruben H. Zamar},
journal= {arXiv preprint arXiv:math/0503665},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009053604000000634 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)