Robust nonparametric confidence intervals and tests for the median in the presence of (c,γ)(c,γ)-contamination

The problem of constructing robust nonparametric confidence intervals and tests for the median is considered when the data distribution is unknown and the data may be contaminated. The (c,γ)(c,γ)-contamination neighborhood which is a generalization of the neighborhoods defined in terms of ɛɛ-contamination and total variation is used to describe the contamination of the data. A modification of the sign test and its associated confidence intervals are proposed, and their robustness and efficiency are studied under the (c,γ)(c,γ)-contamination neighborhood of an absolutely continuous distribution. Some tables and figures of coverage probability and maximum asymptotic length for the confidence intervals are also given.