均值变点模型CUSUM型估计量的相合性  

The consistency of CUSUM-type estimator in mean change-point model

作　　者：刘桓硕 李佳佳 高敏 杨文志[1] LIU Huanshuo;LI Jiajia;GAO Min;YANG Wenzhi(School of Big Data and Statistics,Anhui University,Hefei Anhui 23060l;Wendian College,Anhui University,Hefei Anhui,230601,China)

机构地区：[1]安徽大学大数据与统计学院,安徽收合肥230601 [2]安徽大学文典学院,安徽改合肥230601

出　　处：《阜阳师范大学学报（自然科学版）》2022年第4期7-12,共6页Journal of Fuyang Normal University:Natural Science

基　　金：安徽省自然科学基金面上基金(2008085MA14);安徽省省级“双基”示范项目概率论(Y010512024/032)。

摘　　要：均值变点模型在质量控制等领域应用非常广泛,同时L^r混合鞅是一类重要的鞅结构序列。本文基于误差是L^r混合鞅序列,研究均值变点模型变点位置CUSUM(Cumulative Sum)型估计量的相合性问题。利用均值变点CUSUM型估计量的特点和L^r混合鞅的Hajek-Renyi型不等式,在r阶矩条件(r>2)下,获得了CUSUM型估计量的强收敛速度和弱收敛速度。作为应用,给出了阿里巴巴股价收益率均值变化的实例分析。On the one hand,the mean-variance point model is widely used in the fields of quality control;on the other hand,L^r mixingales is an important class of martingale structure sequences.This paper studies the consistency of the change-point location CUSUM(Cumulative Sum)-type estimator in the mean change-point model based on L^r mixingales.By the characteristics of CUSUM-type estimator and the Hajek-Renyi type inequality of L^r mixingales,the strong convergence rates and weak convergence rates for the CUSUM-type estimator are obtained under the r-th moment condition(r>2).As an application,a real data analysis of mean change for the returns of Alibaba(BABA)stock prices is given.

关 键 词：L^r混合鞅 均值变点模型 CUSUM型估计量 相合性 收敛速度 

分 类 号：O213.1[理学—概率论与数理统计]