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A two-sample test for the equality of univariate marginal distributions for high-dimensional data.

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Title: A two-sample test for the equality of univariate marginal distributions for high-dimensional data.
Authors: Cousido-Rocha, Marta1,2 (AUTHOR) martacousido@uvigo.es, de Uña-Álvarez, Jacobo1,2 (AUTHOR), Hart, Jeffrey D.3 (AUTHOR)
Source: Journal of Multivariate Analysis. Nov2019, Vol. 174, pN.PAG-N.PAG. 1p.
Subjects: Marginal distributions, Data distribution, Univariate analysis, Asymptotic normality, Characteristic functions, Null hypothesis
Abstract: A recurring theme in modern statistics is dealing with high-dimensional data whose main feature is a large number, p , of variables but a small sample size. In this context our aim is to address the problem of testing the null hypothesis that the marginal distributions of p variables are the same for two groups. We propose a test statistic motivated by the simple idea of comparing, for each of the p variables, the empirical characteristic functions computed from the two samples. The asymptotic normality of the test statistic is derived under mixing conditions. In our asymptotic analysis the number of variables tends to infinity, while the size of individual samples remains fixed. In order to obtain a practical test several estimators of the variance are proposed, leading to three somewhat different versions of the test. An alternative global test based on the P -values derived from permutation tests is also proposed. A simulation study to investigate the finite sample properties of the proposed tests is carried out, and a practical illustration involving microarray data is provided. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Multivariate Analysis is the property of Academic Press Inc. 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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  Data: <searchLink fieldCode="DE" term="%22Marginal+distributions%22">Marginal distributions</searchLink><br /><searchLink fieldCode="DE" term="%22Data+distribution%22">Data distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Univariate+analysis%22">Univariate analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+normality%22">Asymptotic normality</searchLink><br /><searchLink fieldCode="DE" term="%22Characteristic+functions%22">Characteristic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Null+hypothesis%22">Null hypothesis</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: A recurring theme in modern statistics is dealing with high-dimensional data whose main feature is a large number, p , of variables but a small sample size. In this context our aim is to address the problem of testing the null hypothesis that the marginal distributions of p variables are the same for two groups. We propose a test statistic motivated by the simple idea of comparing, for each of the p variables, the empirical characteristic functions computed from the two samples. The asymptotic normality of the test statistic is derived under mixing conditions. In our asymptotic analysis the number of variables tends to infinity, while the size of individual samples remains fixed. In order to obtain a practical test several estimators of the variance are proposed, leading to three somewhat different versions of the test. An alternative global test based on the P -values derived from permutation tests is also proposed. A simulation study to investigate the finite sample properties of the proposed tests is carried out, and a practical illustration involving microarray data is provided. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Multivariate Analysis is the property of Academic Press Inc. 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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      – Type: doi
        Value: 10.1016/j.jmva.2019.104537
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Marginal distributions
        Type: general
      – SubjectFull: Data distribution
        Type: general
      – SubjectFull: Univariate analysis
        Type: general
      – SubjectFull: Asymptotic normality
        Type: general
      – SubjectFull: Characteristic functions
        Type: general
      – SubjectFull: Null hypothesis
        Type: general
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      – TitleFull: A two-sample test for the equality of univariate marginal distributions for high-dimensional data.
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            NameFull: Cousido-Rocha, Marta
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            NameFull: de Uña-Álvarez, Jacobo
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            NameFull: Hart, Jeffrey D.
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          Dates:
            – D: 01
              M: 11
              Text: Nov2019
              Type: published
              Y: 2019
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              Value: 174
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            – TitleFull: Journal of Multivariate Analysis
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