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Robust nonparametric inference for the median. (English) Zbl 1057.62035

Summary: 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.

MSC:

62G10 Nonparametric hypothesis testing
62G35 Nonparametric robustness

Keywords:

two-sided test
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