Robust nonparametric confidence intervals and tests for the median in the presence of (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, gamma)-contamination neighborhood which is a generalization of the neighborhoods defined in terms of epsilon-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, gamma)-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. (c) 2008 Elsevier B.V. All rights reserved.