Nonparametric tests for independence: a review and comparative simulation study with an application to malnutrition data in India

Helmut Herwartz, Simone Maxand

Research output: Contribution to journalArticleScientificpeer-review


The detection of dependence structures within a set of random variables provides a valuable basis for a detailed subsequent investigation of their relationships. Nonparametric tests for independence require only basic assumptions on the marginal or joint distribution of the involved variables. In this paper, we review nonparametric tests of independence in bivariate as well as multivariate settings which are throughout ready-to-use, i.e., implemented in R packages. Highlighting their distinct empirical size and power properties in various small sample settings, our analysis supports an analyst in deciding for a most adequate test conditional on underlying distributional settings or data characteristics. Avoiding restrictive moment conditions, the copula based Cramer-von Mises distance of Genest and Remillard (Test 13:335-370,2004) is remarkably robust under the null hypothesis and powerful under diverse settings that are in line with the alternative hypothesis. Based on distinguished test outcomes in small samples, we detect nonlinear dependence structures between childhood malnutrition indices and possible determinants in an empirical application for India.

Original languageEnglish
JournalStatistical Papers
Issue number5
Pages (from-to)2175-2201
Number of pages27
Publication statusPublished - Oct 2020
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 112 Statistics and probability
  • Tests for independence
  • Nonparametric methods
  • Multivariate independence
  • Spatial ranks
  • Empirical copula
  • Distance covariance

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