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An omnibus non‐parametric test of equality in distribution for unknown functions

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  • Alex Luedtke
  • Marco Carone
  • Mark J. van der Laan

Abstract

We present a novel family of non‐parametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described by Gretton and colleagues, using recent developments from the higher order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed quite simply as U‐statistics. We study the asymptotic behaviour of the proposed tests under the null hypothesis and under both fixed and local alternatives. We provide examples to which our tests can be applied and show that they perform well in a simulation study. As an important special case, our proposed tests can be used to determine whether an unknown function, such as the conditional average treatment effect, is equal to zero almost surely.

Suggested Citation

  • Alex Luedtke & Marco Carone & Mark J. van der Laan, 2019. "An omnibus non‐parametric test of equality in distribution for unknown functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(1), pages 75-99, February.
    • Handle: RePEc:bla:jorssb:v:81:y:2019:i:1:p:75-99
    DOI: 10.1111/rssb.12299
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    Cited by:

    1. Kara E. Rudolph & Jonathan Levy & Mark J. van der Laan, 2021. "Transporting stochastic direct and indirect effects to new populations," Biometrics, The International Biometric Society, vol. 77(1), pages 197-211, March.
    2. Bing Li & Constantine Gatsonis & Issa J. Dahabreh & Jon A. Steingrimsson, 2023. "Estimating the area under the ROC curve when transporting a prediction model to a target population," Biometrics, The International Biometric Society, vol. 79(3), pages 2382-2393, September.

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