Consistency of CUSUM estimator for mean change-point model based on ALNQD

In this article, we consider the consistency of the estimator for the mean change-point. In asymptotically linear negative quadrant dependent (ALNQD) case, the limiting distribution is obtained, which extends the results of Bai and Gao et al. Furthermore, based on the estimated change-point location, we derive the limiting distributions of the two mean estimators. Numerical experiments under various settings are provided to validate the theoretical findings. As an application, two real data analyses are presented.