Nonparametric Tests for Multivariate Association

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Testing the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matrix assumptions. Our test is motivated by recent results in MANOVA tests for a large number of groups. Two types of tests are proposed. While it is natural to consider the classical approach for constructing the test by jointly considering all the variables together, we also investigate a composite test where variable-by-variable univariate tests are combined to form a multivariate test. The asymptotic distributions of the test statistics are derived in a unified manner by deriving the asymptotic matrix variate normal distribution of random matrices involved in the construction of the statistics. The tests have good numerical performance in finite samples. The application of the methods is illustrated with gene expression profiling of bronchial airway brushings.

Original languageEnglish
Article number1112
Issue number6
StatePublished - Jun 2022

Bibliographical note

Publisher Copyright:
Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.


  • lack-of-fit test
  • large number of groups
  • multivariate data
  • nonparametric

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)


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