Efficient calculation of p-values in linear-statistic permutation significance tests

@article{Gill2007EfficientCO,
title={Efficient calculation of p-values in linear-statistic permutation significance tests},
author={P. M. Gill},
journal={Journal of Statistical Computation and Simulation},
year={2007},
volume={77},
pages={55 - 61}
}

It is shown that the exact p-values of permutation and bootstrap hypothesis tests of difference between groups can be written as an infinite series whose terms can be computed rapidly, even for large group sizes. Because of connections with the N-step random walk in the plane, the rate of convergence of the series improves as the size of the resampling distribution increases.