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

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.