Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (3): 401-412.doi: 10.3969/j.issn.1005-3085.2022.03.005

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Multiple Mean Change-points Estimation Based on Screening and Ranking Algorithm

LI Yang1,   WU Mixia1,   HU Yao2,   YANG Chao3   

  1. 1. Department of Statistics and Data Science, Faculty of Science, Beijing University of Technology, Beijing 100124 
    2. School of Mathematics and Statistics, Guizhou University, Guiyang 550025 
    3. No.2 High School of Guiyang, Guiyang 550001
  • Online:2022-06-15 Published:2022-08-15
  • Contact: M. Wu. E-mail address: wumixia@bjut.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11661018; 11771032).

Abstract:

The multiple change-points estimation problem is a hot issue in current statistics, and there are many algorithms in the literature. Among them, Screening and Ranking algorithm (SaRa) has attracted wide attention due to its fast detection and high precision characteristics. However, this algorithm tends to be conservative in the threshold selection of the screening procedure. The reason is that the variance in SaRa is separately estimated in each segment process. The main purpose of this paper is to improve SaRa. Firstly, a global estimate of the variance is calculated through local polynomial approximation with the bandwith selected by the cross validation method. The initial change-points are obtained from screening based on the improved threshold. Then, to order those points in terms of the local diagnostic function values, the number of final change-points is determined by maximizing the MBIC. Numerical results show that the proposed algorithm has high accuracies in the estimation of the number and locations of change points in comparison to existing methods. Finally, this method is app-lied to the actual traffic flow data of Shenzhen city. The distribution characteristics of change points on working days and non-working days in this area are analyzed, which can provide some guidance for traffic control departments and travelers.

Key words: multiple mean change-points, local polynomial estimation, cross-validation, screening and ranking, MBIC criterion

CLC Number: