Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process
We first define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-CUSUM process and investigate its theoret...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2294 |
| _version_ | 1797408661427978240 |
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| author | Tadas Danielius Alfredas Račkauskas |
| author_facet | Tadas Danielius Alfredas Račkauskas |
| author_sort | Tadas Danielius |
| collection | DOAJ |
| description | We first define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-CUSUM process and investigate its theoretical aspects including asymptotic behavior. By choosing different sets <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>, we propose some tests for multiple change-point detections in a functional sample. We apply the proposed testing procedures to the real-world neurophysiological data and demonstrate how it can identify the existence of the multiple change-points and localize them. |
| first_indexed | 2024-03-09T04:01:32Z |
| format | Article |
| id | doaj.art-7455d09c6ed44a219c7d8895139b7785 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:01:32Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7455d09c6ed44a219c7d8895139b77852023-12-03T14:12:15ZengMDPI AGMathematics2227-73902022-06-011013229410.3390/math10132294Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum ProcessTadas Danielius0Alfredas Račkauskas1Institute of Applied Mathematics, Vilnius University, 03225 Vilnius, LithuaniaInstitute of Applied Mathematics, Vilnius University, 03225 Vilnius, LithuaniaWe first define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-CUSUM process and investigate its theoretical aspects including asymptotic behavior. By choosing different sets <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>, we propose some tests for multiple change-point detections in a functional sample. We apply the proposed testing procedures to the real-world neurophysiological data and demonstrate how it can identify the existence of the multiple change-points and localize them.https://www.mdpi.com/2227-7390/10/13/2294<i>p</i>-variationfunctional datafunctional change-point detectionfunctional principal component analysis |
| spellingShingle | Tadas Danielius Alfredas Račkauskas Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process Mathematics <i>p</i>-variation functional data functional change-point detection functional principal component analysis |
| title | Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process |
| title_full | Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process |
| title_fullStr | Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process |
| title_full_unstemmed | Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process |
| title_short | Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process |
| title_sort | multiple change point detection in a functional sample via the 𝒢 sum process |
| topic | <i>p</i>-variation functional data functional change-point detection functional principal component analysis |
| url | https://www.mdpi.com/2227-7390/10/13/2294 |
| work_keys_str_mv | AT tadasdanielius multiplechangepointdetectioninafunctionalsampleviathegsumprocess AT alfredasrackauskas multiplechangepointdetectioninafunctionalsampleviathegsumprocess |