On causal estimation using $U$-statistics
提出了一类扩展平均处理效应的因果估计量，通过对比函数量化结果相对优劣，并给出了逆概率加权和双重稳健估计量，适用于有序结果和抗异常值的因果检验。
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.