A Self-Normalized Online Monitoring Method Based on the Characteristic Function
The goal of nonparametric online monitoring methods is to quickly detect structural changes in the distribution of a data stream. This work is concerned with a nonparametric self-normalized monitoring method based on the difference of empirical characteristic functions. This method introduces an add...
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| Format: | Article |
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MDPI AG
2025-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/5/710 |
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| author | Yang Wang Baoying Yang |
| author_facet | Yang Wang Baoying Yang |
| author_sort | Yang Wang |
| collection | DOAJ |
| description | The goal of nonparametric online monitoring methods is to quickly detect structural changes in the distribution of a data stream. This work is concerned with a nonparametric self-normalized monitoring method based on the difference of empirical characteristic functions. This method introduces an additional self-normalization factor, which enables effective control the Type I error. We theoretically investigate the asymptotic properties of the monitoring method under the null hypothesis as well as the alternative hypothesis. Since the asymptotic distribution under the null hypothesis is quite complicated, we apply the multivariate stationary bootstrap method to estimate the critical value of the sequential test. Numerical simulations and a real-world application demonstrate the usefulness of the proposed method. |
| format | Article |
| id | doaj-art-a43a295e60734d8a85f5c17e9daf1b8f |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a43a295e60734d8a85f5c17e9daf1b8f2025-08-20T02:04:48ZengMDPI AGMathematics2227-73902025-02-0113571010.3390/math13050710A Self-Normalized Online Monitoring Method Based on the Characteristic FunctionYang Wang0Baoying Yang1Department of Statistics, School of Mathematics, Southwest Jiaotong University, Chengdu 611756, ChinaDepartment of Statistics, School of Mathematics, Southwest Jiaotong University, Chengdu 611756, ChinaThe goal of nonparametric online monitoring methods is to quickly detect structural changes in the distribution of a data stream. This work is concerned with a nonparametric self-normalized monitoring method based on the difference of empirical characteristic functions. This method introduces an additional self-normalization factor, which enables effective control the Type I error. We theoretically investigate the asymptotic properties of the monitoring method under the null hypothesis as well as the alternative hypothesis. Since the asymptotic distribution under the null hypothesis is quite complicated, we apply the multivariate stationary bootstrap method to estimate the critical value of the sequential test. Numerical simulations and a real-world application demonstrate the usefulness of the proposed method.https://www.mdpi.com/2227-7390/13/5/710empirical characteristic functionself-normalizeddistributional changeonline monitoring |
| spellingShingle | Yang Wang Baoying Yang A Self-Normalized Online Monitoring Method Based on the Characteristic Function Mathematics empirical characteristic function self-normalized distributional change online monitoring |
| title | A Self-Normalized Online Monitoring Method Based on the Characteristic Function |
| title_full | A Self-Normalized Online Monitoring Method Based on the Characteristic Function |
| title_fullStr | A Self-Normalized Online Monitoring Method Based on the Characteristic Function |
| title_full_unstemmed | A Self-Normalized Online Monitoring Method Based on the Characteristic Function |
| title_short | A Self-Normalized Online Monitoring Method Based on the Characteristic Function |
| title_sort | self normalized online monitoring method based on the characteristic function |
| topic | empirical characteristic function self-normalized distributional change online monitoring |
| url | https://www.mdpi.com/2227-7390/13/5/710 |
| work_keys_str_mv | AT yangwang aselfnormalizedonlinemonitoringmethodbasedonthecharacteristicfunction AT baoyingyang aselfnormalizedonlinemonitoringmethodbasedonthecharacteristicfunction AT yangwang selfnormalizedonlinemonitoringmethodbasedonthecharacteristicfunction AT baoyingyang selfnormalizedonlinemonitoringmethodbasedonthecharacteristicfunction |