Regression-adjusted distribution regression for distributional treatment effects under covariate-adaptive randomization is asymptotically normal and attains the semiparametric efficiency bound.
By Assumption 3.1, for all w ∈ W, we have maxs∈S |Dw(s)/n(s)| = op(1), maxs∈S |ˆπw(s) − πw(s)| = op(1), and mins∈S πw(s) > c >0, which imply supy∈Y |I1,1(y)| = op(1)
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On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization
Regression-adjusted distribution regression for distributional treatment effects under covariate-adaptive randomization is asymptotically normal and attains the semiparametric efficiency bound.