时变方差相依序列均值变点的Ratio检验  

Ratio Test of Mean Change Point of Dependent Sequence With Time-varying Variance

作　　者：金浩[1] 李彩彩 白会会 Jin Hao;Li Caicai;Bai Huihui(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,西安710054

出　　处：《统计与决策》2022年第9期46-51,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(71473194);陕西省科技厅自然科学基金资助项目(2020JM513)。

摘　　要：针对时间序列具备时变方差的特点,文章采用Ratio统计量研究了均值变点的检验问题。基于Cavaliere提出的广义中心极限定理,证明在原假设下统计量的渐近分布是广义维纳过程的泛函,并得到在备择假设下的一致性。为消除方差波动性对统计量检验的影响,提出时变方差的估计函数以增强其诊断功效。数值模拟仿真结果表明,基于估计函数的Ratio统计量不仅很好地控制了经验水平,没有出现水平扭曲,而且经验势也有较大的提高。最后,通过一组数据进一步验证了所给出的均值变点检验方法的有效性和可行性。In view of the characteristic of time series with time-varying variance,this paper uses Ratio statistic to study the test on mean change point.On the basis of the generalized central-limit theorem proposed by Cavaliere,the paper proves that asymptotic distribution of the statistic is a functional generalized Wiener process under original hypothesis,and also obtains the consistency under alternative hypothesis.In order to eliminate the influence of variance fluctuation on statistical test,the paper presents the estimation function of time-varying variance to enhance its diagnostic efficacy.The numerical simulation results show that the Ratio statistic based on the estimation function not only controls the empirical level well without horizontal distortion,but also greatly improves the empirical potential.Finally,the paper verifies the validity and feasibility of the proposed test method for mean change point by using a set of data.

关 键 词：均值变点 时变方差 Ratio统计量 方差估计 渐近分布 

分 类 号：O212.1[理学—概率论与数理统计]