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Testing exchangeability of multivariate distributions.

Jan Kalina1,2, Patrik Janáček2

  • 1Institute of Information Theory and Automation, The Czech Academy of Sciences, Prague, Czech Republic.

Journal of Applied Statistics
|November 16, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces multivariate permutation tests for assessing exchangeability in multi-dimensional data. These novel tests are more powerful and suitable than existing methods for complex datasets.

Keywords:
Multivariate distributionexchangeable distributionmultiple comparisonsmultiple testingmultivariate permutation testnon-parametric combination methodology

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Area of Science:

  • Statistics
  • Multivariate Analysis
  • Non-parametric Methods

Background:

  • Existing statistical tests primarily focus on bivariate exchangeability, leaving a gap for multivariate distributions.
  • A need exists for robust methods to test exchangeability in datasets with more than two variables.

Purpose of the Study:

  • To propose and evaluate novel multivariate permutation tests for assessing the exchangeability of multivariate distributions.
  • To address the limitations of existing methods in handling higher-dimensional data.

Main Methods:

  • Development of multivariate permutation tests based on the non-parametric combination methodology.
  • Combining results from non-parametric bivariate exchangeability tests to create a multivariate test.

Main Results:

  • The proposed multivariate permutation tests demonstrate superior power compared to bivariate tests on single variable pairs.
  • These new tests are more suitable than traditional approaches like Benjamini-Yekutieli or Bonferroni for multivariate exchangeability.

Conclusions:

  • Multivariate permutation tests offer a powerful and appropriate solution for assessing exchangeability in high-dimensional data.
  • This work extends non-parametric testing capabilities to complex multivariate statistical distributions.