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Description length and dimensionality reduction in functional data analysis

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dc.contributor.author Poskitt, D.S.
dc.contributor.author Arivalzahan, S.
dc.date.accessioned 2021-11-02T06:41:29Z
dc.date.accessioned 2022-06-28T06:46:04Z
dc.date.available 2021-11-02T06:41:29Z
dc.date.available 2022-06-28T06:46:04Z
dc.date.issued 2011
dc.identifier.uri http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/4093
dc.description.abstract The use of description length principles to select an appropriate number of basis functions for functional data is investigated. A flexible definition of the dimension of a random function that is constructed directly from the Karhunen–Loève expansion of the observed process or data generating mechanism is provided. The results obtained show that although the classical, principle component variance decomposition technique will behave in a coherent manner, in general, the dimension chosen by this technique will not be consistent in the conventional sense. Two description length criteria are described. Both of these criteria are proved to be consistent and it is shown that in low noise settings they will identify the true finite dimension of a signal that is embedded in noise. Two examples, one from mass spectroscopy and the other from climatology, are used to illustrate the basic ideas. The application of different forms of the bootstrap for functional data is also explored and used to demonstrate the workings of the theoretical results. en_US
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.subject Bootstrap en_US
dc.subject Consistency en_US
dc.subject Dimension determination en_US
dc.subject Karhunen–Loève expansion en_US
dc.subject Signal-to-noise ratio en_US
dc.subject Variance decomposition en_US
dc.title Description length and dimensionality reduction in functional data analysis en_US
dc.type Article en_US


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