Combination Test for Mean Shift and Variance Change
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 dis...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/11/1975 |
| _version_ | 1797457697729150976 |
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| author | Min Gao Xiaoping Shi Xuejun Wang Wenzhi Yang |
| author_facet | Min Gao Xiaoping Shi Xuejun Wang Wenzhi Yang |
| author_sort | Min Gao |
| collection | DOAJ |
| description | 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 <b>cpt.meanvar</b> and <b>mosum</b> from the R package, the new method has the advantages of recognition capability and accuracy. |
| first_indexed | 2024-03-09T16:25:43Z |
| format | Article |
| id | doaj.art-8d4dded668a54fdaba834e113dc0123b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:25:43Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8d4dded668a54fdaba834e113dc0123b2023-11-24T15:08:35ZengMDPI AGSymmetry2073-89942023-10-011511197510.3390/sym15111975Combination Test for Mean Shift and Variance ChangeMin Gao0Xiaoping Shi1Xuejun Wang2Wenzhi Yang3School of Big Data and Statistics, Anhui University, Hefei 230601, ChinaIrving K. Barber Faculty of Science, University of British Columbia, Kelowna, BC V1V 1V7, CanadaSchool of Big Data and Statistics, Anhui University, Hefei 230601, ChinaSchool of Big Data and Statistics, Anhui University, Hefei 230601, ChinaThis 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 <b>cpt.meanvar</b> and <b>mosum</b> from the R package, the new method has the advantages of recognition capability and accuracy.https://www.mdpi.com/2073-8994/15/11/1975change-point of meanchange-point of varianceCUSUM estimatorlimit distributionmixing sequences |
| spellingShingle | Min Gao Xiaoping Shi Xuejun Wang Wenzhi Yang Combination Test for Mean Shift and Variance Change Symmetry change-point of mean change-point of variance CUSUM estimator limit distribution mixing sequences |
| title | Combination Test for Mean Shift and Variance Change |
| title_full | Combination Test for Mean Shift and Variance Change |
| title_fullStr | Combination Test for Mean Shift and Variance Change |
| title_full_unstemmed | Combination Test for Mean Shift and Variance Change |
| title_short | Combination Test for Mean Shift and Variance Change |
| title_sort | combination test for mean shift and variance change |
| topic | change-point of mean change-point of variance CUSUM estimator limit distribution mixing sequences |
| url | https://www.mdpi.com/2073-8994/15/11/1975 |
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