Detecting changes in the mean of functional observations
Principal component analysis (PCA) has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t) = µ(t) + 1≤`< ∞ ηi,`v`(t), where µ is the common mean, v ` are the eigenfunctions of the covariance operator, and the ηi, ` are the scores. Inferential procedur...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.536.6033 2023-05-15T16:29:14+02:00 Detecting changes in the mean of functional observations Robertas Gabrys Piotr Kokoszka The Pennsylvania State University CiteSeerX Archives application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.536.6033 http://wami.usu.edu/files/uploads/publications/bb.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.536.6033 http://wami.usu.edu/files/uploads/publications/bb.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://wami.usu.edu/files/uploads/publications/bb.pdf Change point detection Functional data analysis Mean of functional data Significance test Abbreviated Title Changes in functional mean text ftciteseerx 2016-01-08T10:50:40Z Principal component analysis (PCA) has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t) = µ(t) + 1≤`< ∞ ηi,`v`(t), where µ is the common mean, v ` are the eigenfunctions of the covariance operator, and the ηi, ` are the scores. Inferential procedures assume that the mean function µ(t) is the same for all values of i. If, in fact, the observations do not come from one population, but rather their mean changes at some point(s), the results of PCA are confounded by the change(s). It is therefore important to develop a methodol-ogy to test the assumption of a common functional mean. We develop such a test using quantities which can be readily computed in the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymp-totic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from Prague, England and Greenland. Text Greenland Unknown Greenland |
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Change point detection Functional data analysis Mean of functional data Significance test Abbreviated Title Changes in functional mean |
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Change point detection Functional data analysis Mean of functional data Significance test Abbreviated Title Changes in functional mean Robertas Gabrys Piotr Kokoszka Detecting changes in the mean of functional observations |
topic_facet |
Change point detection Functional data analysis Mean of functional data Significance test Abbreviated Title Changes in functional mean |
description |
Principal component analysis (PCA) has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t) = µ(t) + 1≤`< ∞ ηi,`v`(t), where µ is the common mean, v ` are the eigenfunctions of the covariance operator, and the ηi, ` are the scores. Inferential procedures assume that the mean function µ(t) is the same for all values of i. If, in fact, the observations do not come from one population, but rather their mean changes at some point(s), the results of PCA are confounded by the change(s). It is therefore important to develop a methodol-ogy to test the assumption of a common functional mean. We develop such a test using quantities which can be readily computed in the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymp-totic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from Prague, England and Greenland. |
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The Pennsylvania State University CiteSeerX Archives |
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Text |
author |
Robertas Gabrys Piotr Kokoszka |
author_facet |
Robertas Gabrys Piotr Kokoszka |
author_sort |
Robertas Gabrys |
title |
Detecting changes in the mean of functional observations |
title_short |
Detecting changes in the mean of functional observations |
title_full |
Detecting changes in the mean of functional observations |
title_fullStr |
Detecting changes in the mean of functional observations |
title_full_unstemmed |
Detecting changes in the mean of functional observations |
title_sort |
detecting changes in the mean of functional observations |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.536.6033 http://wami.usu.edu/files/uploads/publications/bb.pdf |
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Greenland |
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Greenland |
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Greenland |
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Greenland |
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.536.6033 http://wami.usu.edu/files/uploads/publications/bb.pdf |
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