Permutation testing in high-dimensional linear models: an empirical investigation

Jesse Hemerik*, Magne Thoresen, Livio Finos

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates. Permutation-based tests are valuable in particular because they can be highly robust to violations of the standard linear model, such as non-normality and heteroscedasticity. Moreover, in some cases they can be combined with existing, powerful permutation-based multiple testing methods. Here, we propose permutation tests for models where the number of nuisance coefficients exceeds the sample size. The performance of the novel tests is investigated with simulations. In a wide range of simulation scenarios our proposed permutation methods provided appropriate type I error rate control, unlike some competing tests, while having good power.

Original languageEnglish
JournalJournal of Statistical Computation and Simulation
Publication statusE-pub ahead of print - Nov 2020


  • group invariance test
  • heteroscedasticity
  • high-dimensional
  • Permutation test
  • semi-parametric

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