Robust estimation of change-point location

Abstract

We introduce a robust estimator of the location parameter for the change-point in the mean based on the Wilcoxon statistic and establish its consistency for L1 near epoch dependent processes. It is shown that the consistency rate depends on the magnitude of change. A simulation study is performed to evaluate finite sample properties of the Wilcoxon-type estimator in standard cases, as well as under heavy-tailed distributions and disturbances by outliers, and to compare it with a CUSUM-type estimator. It shows that the Wilcoxon-type estimator is equivalent to the CUSUM-type estimator in standard cases, but outperforms the CUSUM-type estimator in presence of heavy tails or outliers in the data.