Distribution-free tests of independence in high dimensions

Fang Han, Shizhe Chen, Han Liu

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We consider the testing of mutual independence among all entries in a d-dimensional random vector based on n independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and Spearman's rho as important examples.We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where d > n.We further show that the two tests are rate-optimal in terms of power against sparse alternatives and that they outperform competitors in simulations, especially when d is large.

Original languageEnglish (US)
Pages (from-to)813-828
Number of pages16
JournalBiometrika
Volume104
Issue number4
DOIs
StatePublished - Dec 1 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Gumbel distribution
  • Kendall's tau
  • Linear rank statistic
  • Mutual independence
  • Rank-typeU-statistic
  • Spearman's rho

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