Multiple permutation test for high-dimensional data: a components-combined algorithm

Wei Yu, Wangli Xu, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


Multiple permutation testing is a test method combining the idea of permutation and multiple testing. It first employs the permutation testing to calculate p-values for single tests, and then determines the result based on criteria of multiple testing. To well control type I error rate, the classical method needs a large number of permutation samples for calculating p-values. When the dimension of data, m, is high, the permutation procedure is very time consuming. This paper proposes a components-combined algorithm for the type I error rate control. The new algorithm only requires a small and fixed number of permutation samples for any dimension of data and can achieve the same approximation accuracy of p-values as the classical method. Therefore, it reduces the computational amount of multiple permutation testing procedures from O(m2) to O(m).. The algorithm is then applied to several testing problems and the power performance is examined by simulations and comparisons with existing methods.

Original languageEnglish
Pages (from-to)686-707
Number of pages22
JournalJournal of Statistical Computation and Simulation
Issue number4
Publication statusPublished - 4 Mar 2019

Scopus Subject Areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Components-combined algorithm
  • correlation matrices testing
  • mean testing
  • multiple permutation testing
  • type I error rate


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