Robust Wilcoxon‐Type Estimation of Change‐Point Location Under Short‐Range Dependence

Abstract

We introduce a robust estimator of the location parameter for the change‐point in the mean based on Wilcoxon statistic and establish its consistency for L1 near‐epoch dependent processes. It is shown that the consistency rate depends on the magnitude of the change. A simulation study is performed to evaluate the finite sample properties of the Wilcoxon‐type estimator under Gaussianity 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 under Gaussianity but outperforms it in the presence of heavy tails or outliers in the data.

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