  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.
