An assumption-free exact test for fixed-design linear models with exchangeable errors

@article{Lei2019AnAE,
  title={An assumption-free exact test for fixed-design linear models with exchangeable errors},
  author={Lihua Lei and Peter J. Bickel},
  journal={arXiv: Methodology},
  year={2019}
}
We propose the cyclic permutation test (CPT) to test general linear hypotheses for linear models. This test is non-randomized and valid in finite samples with exact type-I error $\alpha$ for arbitrary fixed design matrix and arbitrary exchangeable errors, whenever $1 / \alpha$ is an integer and $n / p \ge 1 / \alpha - 1$. The test applies the marginal rank test on $1 / \alpha$ linear statistics of the outcome vectors where the coefficient vectors are determined by solving a linear system such… 

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