Strong convergence rate of robust estimator of change point

This paper considers a mean shift with a unknown change point in α-mixing processes with κ stable innovations and estimates the unknown change point by the robust nonparametric CUSUM estimator based on the indicators of the data minus the sample median. The strong convergence rate of the estimator is obtained, which is not affected by the characteristic index κ. We also develop two algorithms for the estimate of change point based on the proposed CUSUM estimator. Simulations demonstrate that the estimator behaves well for heavy-tailed sequences.