Robust non parametric inference for the median

VÍCTOR J. YOHAI; RUBÉN ZAMAR

ANNALS OF STATISTICS, THE

Institute of Mathematical Statistics

Lugar: Beachwood, OH , USA; Año: 2004 vol. 32 p. 1841 - 1857

0090-5364

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.