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

Sung Nok Chiu, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Kwong Ip Liu, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

Abstract

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.