The consistency for CUSUM estimator of mean change-point model based on association

Abstract

This article studies the CUSUM estimators of the mean change-point based on the association errors and obtains some important consistency results. For example, the weak and strong convergence rates as well as the limit distribution are obtained for the estimators of the mean change-point and mean parameter. We extend the existing results of mean change points, and give some simulations with Normality and multivariate t distribution errors. As an application, two real data examples are provided to illustrate the analysis of the mean change-point.

Keywords:

• CUSUM
• mean change-point
• convergence rates
• asymptotic distribution
• associated sequences

Acknowledgments

The authors are deeply grateful to editors and anonymous referees for their carefully read and insightful comments. The comments led us to significantly improve the paper.

Disclose statement

The author has no conflict of interest to disclose.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11901149), the Natural Science Foundation of Anhui Province (2008085MA14, 2108085MA06), and the Quality Engineering Programme of Anhui Province (2022jyjxggyj113).