Quantile Treatment Effects and Bootstrap Inference under Covariate-Adaptive Randomization
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This paper studies the estimation and inference of the quantile treatment effect under covariate-adaptive randomization. We propose three estimation methods: (1) the simple quantile regression (QR), (2) the QR with strata fixed effects, and (3) the inverse propensity score weighted QR. For the three estimators, we derive their asymptotic distributions uniformly over a set of quantile indexes and show that the estimator obtained from inverse propensity score weighted QR weakly dominates the other two in terms of efficiency, for a wide range of randomization schemes. For inference, we show that the weighted bootstrap tends to be conservative for methods (1) and (2) while has asymptotically exact type I error for method (3). We also show that the covariate-adaptive bootstrap inference is valid for all three methods. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.
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