Improving p-value approximation and level accuracy of Monte Carlo tests by quasi-Monte Carlo methods

We argue and show empirically that for the Monte Carlo test, if the pseudo-random numbers are replaced by a randomized low discrepancy sequence, the actual errors in approximating the p-value are smaller and the deviations of the exact level from the nominal level have higher potential to be smaller. Hence in real applications the proposed method, called randomized quasi-Monte Carlo test, is suggested to be used instead of the traditional Monte Carlo test.