Ratio detections for change point in heavy tailed observations

Abstract

This article modifies the ratio test so that we can detect the change which happens in the latter half observations effectively. Moreover, we propose a new ratio test on the self-normalized numerator and the self-normalized denominator respectively. We establish the asymptotic properties under the null and alternative hypotheses. We also propose a new estimator to locate the early or later change. We check the theoretical validity of the block bootstrap approximation for the modified tests and give the weak convergence of the proposed estimator. Simulations demonstrate the validity of the block bootstrap procedures and the advantage of the proposed estimator. An application on a real data is illustrated for the practicability of the proposed test and the estimators.

Keywords:

• Block bootstrap
• change point
• heavy-tailed
• ratio test
• self-normalization

Acknowledgment

The authors would like to thank the editor and the referees for their suggestions, which improved this manuscript greatly.

Additional information

Funding

Financial supports from the National Natural Science Foundation of China (No.11661067,61807022,71971131) are gratefully acknowledged. This work is also supported by the Natural Science Foundation of Shanxi Province (201801D121005), the Natural Science Foundation of Qinghai Province (No. 2019-ZJ-920), and Research Project Supported by Shanxi Scholarship Council of China (2016-015), the Humanity and Social Science Foundation of Ministry of Education of China (No. 18YJC910009).