Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process

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...

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Bibliographic Details
Main Authors: Tadas Danielius, Alfredas Račkauskas
Format: Article
Language:English
Published: MDPI AG 2022-06-01
Series:Mathematics
Subjects:
<i>p</i>-variation
functional data
functional change-point detection
functional principal component analysis
Online Access:https://www.mdpi.com/2227-7390/10/13/2294
Description
Summary: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.
ISSN:2227-7390

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