A permutation-based framework for testing the association of a covariate of interest with a response, adjusted for control covariates, that provably controls the finite-sample type I error rate even when the noise is heavy-tailed or skewed. Its novel contribution is separating model-fitting from model-evaluation: the model may be fit by ordinary, robust, or quantile regression (with hyper-parameter tuning), while a robust loss used only in the evaluation step improves power regardless of how the model was fit. Fitting multiple models lets the framework target specialized distributional features, as in DispersionPALMRT for detecting differences in dispersion between groups. Demonstrated on Long-COVID immunological data.
Introduces RobustPALMRT, a permutation framework for testing whether a covariate of interest is associated with a response after adjusting for control covariates in a linear model, motivated by heavy…