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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Main Authors: Yang Wang, Baoying Yang
Format: Article
Language:English
Published: MDPI AG 2025-02-01
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.
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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
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AT baoyingyang aselfnormalizedonlinemonitoringmethodbasedonthecharacteristicfunction
AT yangwang selfnormalizedonlinemonitoringmethodbasedonthecharacteristicfunction
AT baoyingyang selfnormalizedonlinemonitoringmethodbasedonthecharacteristicfunction