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Projection pursuit based tests of normality with functional data.

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Title: Projection pursuit based tests of normality with functional data.
Authors: Kolkiewicz, Adam1 (AUTHOR), Rice, Gregory1 (AUTHOR), Xie, Yijun1 (AUTHOR) yijun.xie@uwaterloo.ca
Source: Journal of Statistical Planning & Inference. Mar2021, Vol. 211, p326-339. 14p.
Subjects: Data modeling, Algorithms, Data analysis, Computational statistics, Data
Abstract: Methods for validating the assumption of normality of functional data have been only lightly developed to date, with existing methods based primarily on summarizing the data by their projections into random or principal component subspaces, and applying multivariate normality tests to the vectors of scores defining these projections. While this is effective in some cases, we show with both real and synthetic data examples some pitfalls of this approach, including their sensitivity to the basis used to smooth the raw data. We propose a new normality test for functional data based on a projection pursuit that overcomes some of these challenges. Asymptotic theory is developed for the proposed statistics, and we develop several new computational tools needed to implement the high-dimensional projection pursuit. As a by-product of evaluating the test statistic, our method furnishes a way of decomposing functional data into its approximately Gaussian and non-Gaussian components, which is useful for the purpose of data visualization and subsequent analyses. A simulation study and analysis of three data sets demonstrate the complimentary advantages of the proposed test to those currently available in the literature. • A robust and consistent functional normality test. • A novel algorithm for projection pursuit in functional and high dimensional spaces is proposed. • Results may be interpreted as identifying the least Gaussian projections of the data. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 146073804
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  Data: Projection pursuit based tests of normality with functional data.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Planning+%26+Inference%22">Journal of Statistical Planning & Inference</searchLink>. Mar2021, Vol. 211, p326-339. 14p.
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  Label: Abstract
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  Data: Methods for validating the assumption of normality of functional data have been only lightly developed to date, with existing methods based primarily on summarizing the data by their projections into random or principal component subspaces, and applying multivariate normality tests to the vectors of scores defining these projections. While this is effective in some cases, we show with both real and synthetic data examples some pitfalls of this approach, including their sensitivity to the basis used to smooth the raw data. We propose a new normality test for functional data based on a projection pursuit that overcomes some of these challenges. Asymptotic theory is developed for the proposed statistics, and we develop several new computational tools needed to implement the high-dimensional projection pursuit. As a by-product of evaluating the test statistic, our method furnishes a way of decomposing functional data into its approximately Gaussian and non-Gaussian components, which is useful for the purpose of data visualization and subsequent analyses. A simulation study and analysis of three data sets demonstrate the complimentary advantages of the proposed test to those currently available in the literature. • A robust and consistent functional normality test. • A novel algorithm for projection pursuit in functional and high dimensional spaces is proposed. • Results may be interpreted as identifying the least Gaussian projections of the data. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1016/j.jspi.2020.07.001
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 326
    Subjects:
      – SubjectFull: Data modeling
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Data analysis
        Type: general
      – SubjectFull: Computational statistics
        Type: general
      – SubjectFull: Data
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      – TitleFull: Projection pursuit based tests of normality with functional data.
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            NameFull: Kolkiewicz, Adam
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            NameFull: Rice, Gregory
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            NameFull: Xie, Yijun
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          Dates:
            – D: 01
              M: 03
              Text: Mar2021
              Type: published
              Y: 2021
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              Value: 211
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            – TitleFull: Journal of Statistical Planning & Inference
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