The CUSUM statistic of change point under NA sequences
NA序列下变化点的CUSUM统计量
NAシーケンスでの変化点のCUSUM統計
NA 시퀀스에서 변화점의 CUSUM 통계
La estadística CUSUM del punto de cambio bajo secuencias NA
La statistique CUSUM du point de changement sous les séquences NA
Статистика CUSUM точки изменения при последовательностях NA
Jin Ling ¹, Xiao-qin Li 李晓琴 ², Wen-zhi Yang 杨文志 ², Jian-ling Jiao 焦建玲 ¹
¹ School of Management, Hefei University of Technology, Hefei, 230009, China
中国 合肥 合肥工业大学管理学院
² Center for Applied Mathematics, School of Mathematical Sciences, Anhui University, Hefei, 230061, China
中国 合肥 安徽大学数学科学学院 应用数学中心
Applied Mathematics-A Journal of Chinese Universities, 22 December 2021
Abstract
In this paper, we investigate the CUSUM statistic of change point under the negatively associated (NA) sequences. By establishing the consistency estimators for mean and covariance functions respectively, the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge, which extends the results obtained under the case of an independent normal sample and the moving average processes.
Finally, the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.
