基于Bootstrap方法的重尾相依序列均值变点Ratio检验  

Ratio Tests for Mean Break With Heavy-tailed Dependent Sequence Based on Bootstrap Method

作　　者：金浩[1] 高奎 张思[1] Jin Hao;Gao Kui;Zhang Si(School of Science,Xi'an University of Science and Technology,Xi'an 710054,China)

机构地区：[1]西安科技大学理学院

出　　处：《统计与决策》2019年第23期11-16,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(71473194;71273206);陕西省科技厅自然科学基金资助项目(2013KJXX-40;2017JM1024);陕西省教育厅科学研究计划资助项目(16JK1500)

摘　　要：文章提出了一个改进的Ratio统计量来检测方差无穷重尾相依序列中可能存在的均值变点。基于广义泛函中心极限定理,在原假设下得到统计量的渐近分布,并在备择假设下证明了该检验的一致性。针对重尾指数未知且难以估计的特点,应用Bootstrap重抽样方法确定了统计量渐近分布的临界值。数值模拟结果表明:Ratio检验不仅能很好地控制经验水平,而且相比已有的均值变点检验方法,经验势也有较·明显的提高.This paper proposes a modified ratio test to detect the possible mean variation points under heavy-tailed dependent sequence with infinite variance. On the basis of general functional central limit theorem,and under the null hypothesis the asymptotic distribution of statistics is deduced, and the consistency of the test is proved under the alternative hypothesis. Finally,aiming at features that the heavy tail index is unknown and difficult to estimate, the paper uses Bootstrap repeated sampling method to determine the critical value of statistic asymptotic distribution. Numerical simulations indicate that the Ratio test can not only control the empirical level well, but also significantly improve the empirical potential, compared with the existing test method for the mean break.

关 键 词：重尾序列 均值变点 Ratio统计量 BOOTSTRAP 渐近分布 

分 类 号：O212[理学—概率论与数理统计]