# Robust Estimation of Change-Point Location

## TL;DR

This paper proposes a robust Wilcoxon-based estimator for change-point location in mean, demonstrating its consistency and superior performance over CUSUM in heavy-tailed and contaminated data scenarios.

## Contribution

It introduces a Wilcoxon-type estimator for change-point detection that is robust to heavy tails and outliers, with proven consistency and improved finite sample performance.

## Key findings

- Wilcoxon estimator is consistent for $L_1$ near epoch dependent processes.
- Performs comparably to CUSUM in standard cases.
- Outperforms CUSUM under heavy tails and outliers.

## 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 $L_1$ 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.