Permutation testing in high-dimensional linear models: an empirical investigation. Issue 5 (24th March 2021)

• Record Type: Journal Article
• Authors: Hemerik, Jesse; Thoresen, Magne; Finos, Livio
• Is Part Of: Journal of statistical computation and simulation. Volume 91:Issue 5(2021)
• Page Start: 897
• Page End: 914
• Publication Date: 2021-03-24
• Subjects: Permutation test -- group invariance test -- high-dimensional -- heteroscedasticity -- semi-parametric; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2020.1836183
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : 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.