Convergence rate of location parameter change-point estimator

For the location parameter change point model allowing at most one change, an antisymmetric kernel function was constructed and a change point estimator was proposed with the help of the CUSUM method. The consistency and convergence rate of the change point estimator were studied under normal conditions and its consistency was given under the condition of local alternative hypothesis. Finally, simulation was performed under different sample sizes and parameter settings. From the histograms, the closer the change-point location gets to the middle, the more accurate the estimate is. The results show that our methods are effective.