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A simple method for implementing Monte Carlo tests

Author

Listed:
  • Dong Ding

    (Imperial College London)

  • Axel Gandy

    (Imperial College London)

  • Georg Hahn

    (Lancaster University)

Abstract

We consider a statistical test whose p value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p value for an observed data set lies above or below a given threshold such as 5%. We want to ensure that the resampling risk, the probability of the (Monte Carlo) decision being different from the true decision, is uniformly bounded. This article introduces a simple open-ended method with this property, the confidence sequence method (CSM). We compare our approach to another algorithm, SIMCTEST, which also guarantees an (asymptotic) uniform bound on the resampling risk, as well as to other Monte Carlo procedures without a uniform bound. CSM is free of tuning parameters and conservative. It has the same theoretical guarantee as SIMCTEST and, in many settings, similar stopping boundaries. As it is much simpler than other methods, CSM is a useful method for practical applications.

Suggested Citation

  • Dong Ding & Axel Gandy & Georg Hahn, 2020. "A simple method for implementing Monte Carlo tests," Computational Statistics, Springer, vol. 35(3), pages 1373-1392, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-019-00927-6
    DOI: 10.1007/s00180-019-00927-6
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    References listed on IDEAS

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