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