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

Sung Nok Chiu; Kwong Ip Liu

doi:10.1080/03610918.2019.1667389

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

Sung Nok Chiu^*, Kwong Ip Liu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

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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.

Original language	English
Pages (from-to)	1272-1288
Number of pages	17
Journal	Communications in Statistics - Simulation and Computation
Volume	51
Issue number	3
Early online date	20 Sept 2019
DOIs	https://doi.org/10.1080/03610918.2019.1667389
Publication status	Published - Mar 2022

Scopus Subject Areas

Statistics and Probability
Modelling and Simulation

User-Defined Keywords

Monte Carlo test
Quasi-Monte Carlo
Resampling
Sobol’ sequence

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10.1080/03610918.2019.1667389

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AB - 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.

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

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