含测量误差的方差模型的多变点的估计
Estimation of Variable Points of Variance Model with Measurement Error
DOI: 10.12677/AAM.2024.132083, PDF,    科研立项经费支持
作者: 沙达克提·艾力：新疆师范大学数学科学学院，新疆 乌鲁木齐
关键词: 测量误差；方差变点；调节参数；相合性；二元分割法；Measurement Error； Variance Change Point； Adjustment Parameters； Consistency； Binary Segmentation Method
摘要: 本文讨论当已知含测量误差的方差模型存在变点时，对方差变点给出了一个含有调节参数的“CUSUM型估计量”，研究了方差变点统计量的弱(强)相合性，得到收敛速度。结合“二元分割法”将其推广至多个方差变点的估计。模拟研究发现含调节参数γ∈(0.3,0.7)的CUSUM型估计量的精确度要优于无调节参数(γ=0)的CUSUM型估计量的精确度。进一步，对原油价格涨跌幅进行实证分析验证了本文方法的有效性和可行性。
Abstract: This article discusses when it is known that variance models with measurement errors have change points, a “CUSUM-type estimator” with adjustment parameters is given for the variance change point. The weak (strong) consistency of variance change point estimator is studied, and the conver-gence rate is obtained. It is extended to the estimation of multiple variance change points by using binary segmentation method. The simulation results show that the accuracy of CUSUM type estima-tor with adjustment parameter γ∈(0.3,0.7) is better than that of CUSUM type estimator without adjustment parameter γ=0 . Furthermore, the validity and feasibility of this method are verified by an empirical analysis of the rise and fall of crude oil prices.
文章引用：沙达克提·艾力. 含测量误差的方差模型的多变点的估计[J]. 应用数学进展, 2024, 13(2): 877-890. https://doi.org/10.12677/AAM.2024.132083

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