Combination Test for Mean Shift and Variance Change

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-10-25 DOI:10.3390/sym15111975
Min Gao, Xiaoping Shi, Xuejun Wang, Wenzhi Yang
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Abstract

This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the limiting distributions for the mean change test and variance change test. As an application, an algorithm for a three-step method to detect the change-points is given. For example, the first step is to test whether there is at least a change-point. The second and third steps are to detect the mean change-point and the variance change-point, respectively. To illustrate our results, some simulations and real-world data analysis are discussed. The analysis shows that our tests not only have high powers, but can also determine the mean change-point or variance change-point. Compared to the existing methods of cpt.meanvar and mosum from the R package, the new method has the advantages of recognition capability and accuracy.
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均值移位和方差变化的组合检验
本文考虑了一种新的强混合误差均值-方差模型,并给出了均值移位和方差变化的组合检验方法。在一定的平稳性和对称性条件下,得到了组合检验的重要极限分布,从而导出了均值变化检验和方差变化检验的极限分布。作为应用,给出了一种三步法检测变化点的算法。例如,第一步是测试是否至少存在一个变更点。第二步和第三步分别检测均值变化点和方差变化点。为了说明我们的结果,讨论了一些模拟和实际数据分析。分析表明,我们的测试不仅具有较高的功率,而且可以确定平均变化点或方差变化点。与现有的cpt方法相比。基于R包的均值和最小值,该方法具有识别能力强、精度高的优点。
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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