Distributed estimation and its fast algorithm for change-point in location models*

Abstract

Change point detection has been widely used in quality control, earthquake disaster prediction and other fields. Existing change-point analysis methods rarely take into account the computational complexity, memory requirements and privacy issues under large data size. In this paper, we propose a distributed fast algorithm for change-point estimation when data are divided into many computers. Based on a subsequence data stored in one single machine, we get a change-point pre-estimator which is used to construct an interval covering the true change point with large probability, and then search the change-point more precisely on this interval among all machines. The final estimator by the above algorithm is proved to have consistency and limiting distribution with the same performance under the data-centralized case. The effectiveness of our algorithm is verified by sufficient numerical experiments which show that the asymptotic properties of our method are very close to that of traditional one, but with much less computation time.

KEYWORDS:

• Change point
• distributed fast algorithm
• least-squares estimation
• consistency
• convergence rate
• limiting distribution

Additional information

Funding

This study was funded by National Natural Science Foundation of China [Grant number 11771353].