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On causal estimation using $U$-statistics

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  • Lu Mao

Abstract

Summary We introduce a general class of causal estimands which extends the familiar notion of average treatment effect. The class is defined by a contrast function, prespecified to quantify the relative favourability of one outcome over another, averaged over the marginal distributions of two potential outcomes. Natural estimators arise in the form of $U$-statistics. We derive both a naive inverse propensity score weighted estimator and a class of locally efficient and doubly robust estimators. The usefulness of our theory is illustrated by two examples, one for causal estimation with ordinal outcomes, and the other for causal tests that are robust with respect to outliers.

Suggested Citation

  • Lu Mao, 2018. "On causal estimation using $U$-statistics," Biometrika, Biometrika Trust, vol. 105(1), pages 215-220.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:1:p:215-220.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx071
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    Cited by:

    1. Mao, Lu, 2022. "Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. Bryan S. Graham, 2019. "Network Data," NBER Working Papers 26577, National Bureau of Economic Research, Inc.
    3. Juan Carlos Escanciano & Joel Robert Terschuur, 2022. "Machine Learning Inference on Inequality of Opportunity," Papers 2206.05235, arXiv.org, revised Oct 2023.
    4. Bryan S. Graham, 2019. "Network Data," CeMMAP working papers CWP71/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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