一种线性过程方差变点的比率检验  

Ratio Test for the Variance Change Point of Linear Process

作　　者：秦瑞兵[1] 游悦 QIN Ruibing;YOU Yue(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,太原030006

出　　处：《河南科学》2020年第1期33-40,共8页Henan Science

基　　金：山西省自然科学基金(201801D121005);青海省2019年基础研究计划项目(2019-ZJ-920)。

摘　　要：针对现有的用于线性过程中方差变点的比率检验存在势过低的问题,提出了一种新的检验统计量.同时研究了该统计量在原假设下的渐近分布以及备择假设下的渐近性质.此外提出一种新的变点估计方法,建立了该变点估计方法的收敛性和收敛速度.蒙特卡罗模拟表明了该统计量在样本量大小适中时比原统计量具有更好的经验水平和更高的势,所提出的估计方法也具有一致性.最后通过实例分析验证了该方法的有效性.A new test statistic is proposed to solve the problem of low potential in the ratio test of the variance change point in linear process.At the same time,the asymptotic distribution under the null hypothesis and the asymptotic property under the alternative hypothesis of the statistic are studied.In addition,a new method of change point estimation is proposed,and the convergence and convergence speed of that method are established.Monte Carlo simulation shows that the statistic has better empirical level and higher potential than the original statistic when the sample size is moderate,and the proposed estimation method in this paper is also consistent.Finally,the effectiveness of the method is verified by case analysis.

关 键 词：比例检验 线性过程 方差变点 变点估计 一致性检验 收敛速度 

分 类 号：O212[理学—概率论与数理统计]