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The average treatment effect, which is the difference in expectation of thecounterfactuals, is probably the most popular target effect in causal inferencewith binary treatments. However, treatments may have effects beyond the mean,for instance decreasing or increasing the variance. We propose a newkernel-based test for distributional effects of the treatment. It is, to thebest of our knowledge, the first kernel-based, doubly-robust test with provablyvalid type-I error. Furthermore, our proposed algorithm is computationallyefficient, avoiding the use of permutations.

An Efficient Doubly-Robust Test for the Kernel Treatment Effect