Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization

Zhang, Yichong; Zheng, Xin

doi:10.3982/qe1323

Cited by 17 publications

(8 citation statements)

References 33 publications

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“…Note that L w 2,n (τ ) is exactly the same as that considered in the proof of Theorem 3.2 in Zhang and Zheng (2020) and by their result we have sup…”

Section: G Proof Of Theorem 41mentioning

confidence: 79%

“…For completeness, we briefly repeat their descriptions below. Note we only require D n (s)/n(s) = o p (1), which is weaker than the assumption imposed by Bugni et al (2018) but the same as that imposed by Bugni et al (2019) and Zhang and Zheng (2020).…”

Section: Setup and Notationmentioning

confidence: 99%

“…Bugni, Canay, and Shaikh (2018) extended the framework to the nonparametric setup, proposed an adjusted standard error for the ATE estimator, and considered a permutation test. Zhang and Zheng (2020) showed that, under CARs, the standard bootstrap inference for the QTE is conservative under the null and lacks power under the alternative. Instead, they suggested multiplier bootstrapping the inverse propensity score weighted (IPW) estimator of the QTE and showed that the distribution of the bootstrap estimator can mimic the original one under CARs.…”

Section: Introductionmentioning

confidence: 99%

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Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations

Jiang¹,

Phillips²,

Tao³

et al. 2021

Preprint

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This paper examines regression-adjusted estimation and inference of unconditional quantile treatment effects (QTEs) under covariate-adaptive randomizations (CARs). Datasets from field experiments usually contain extra baseline covariates in addition to the strata indicators. We propose to incorporate these extra covariates via auxiliary regressions in the estimation and inference of unconditional QTEs. We establish the consistency, limit distribution, and validity of the multiplier bootstrap of the QTE estimator under CARs. The auxiliary regression may be estimated parametrically, nonparametrically, or via regularization when the data are high-dimensional. Even when the auxiliary regression is misspecified, the proposed bootstrap inferential procedure still achieves the nominal rejection probability in the limit under the null. When the auxiliary regression is correctly specified, the regression-adjusted estimator achieves the minimum asymptotic variance. We also derive the optimal pseudo true values for the potentially misspecified parametric model that minimize the asymptotic variance of the corresponding QTE estimator. Our estimation and inferential methods can be implemented without tuning parameters and they allow for common choices of auxiliary regressions such as linear, probit and logit regressions despite the fact that these regressions may be misspecified. Finite-sample performance of the new estimation and inferential methods is assessed in simulations and an empirical application studying the impact of child health and nutrition on educational outcomes is included.

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“…Note that L w 2,n (τ ) is exactly the same as that considered in the proof of Theorem 3.2 in Zhang and Zheng (2020) and by their result we have sup…”

Section: G Proof Of Theorem 41mentioning

confidence: 79%

Section: Setup and Notationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations

Jiang¹,

Phillips²,

Tao³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…For completeness, we briefly repeat their descriptions below. Note we only require B n (s)/n(s) = o p (1), which is weaker than the assumption imposed by Bugni et al (2018) but the same as that imposed by Bugni et al (2019) and Zhang and Zheng (2020). Fourth, Assumption 1(v) implies there are no defiers.…”

Section: Setupmentioning

confidence: 99%

“…Our paper is related to several lines of research. Bugni et al (2018); Bugni, Canay, and Shaikh (2019); Hu and Hu (2012); Ma, Hu, and Zhang (2015); Ma, Qin, Li, and Hu (2020); Olivares (2021); Shao and Yu (2013); Shao, Yu, and Zhong (2010); Zhang and Zheng (2020); Ye (2018); Ye and Shao (2020) studied inference of either ATEs or QTEs under CARs without considering additional covariates. Bloniarz, Liu, Zhang, Sekhon, and Yu (2016); Fogarty (2018); Lin (2013); Lu (2016); Lei and Ding (2021); Li and Ding (2020); Liu, Tu, and Ma (2020); Liu and Yang (2020); Negi and Wooldridge (2020); Ye, Yi, and Shao (2021); Zhao and Ding (2021) studied the estimation and inference of ATEs using a variety of regression regression methods under various randomization.…”

Section: Introductionmentioning

confidence: 99%

Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance

Jiang¹,

Linton²,

Tang³

et al. 2022

Preprint

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We study regression adjustments with additional covariates in randomized experiments under covariate-adaptive randomizations (CARs) when subject compliance is imperfect. We develop a regression-adjusted local average treatment effect (LATE) estimator that is proven to improve efficiency in the estimation of LATEs under CARs. Our adjustments can be parametric in linear and nonlinear forms, nonparametric, and high-dimensional. Even when the adjustments are misspecified, our proposed estimator is still consistent and asymptotically normal, and their inference method still achieves the exact asymptotic size under the null. When the adjustments are correctly specified, our estimator achieves the minimum asymptotic variance. When the adjustments are parametrically misspecified, we construct a new estimator which is weakly more efficient than linearly and nonlinearly adjusted estimators, as well as the one without any adjustments. Simulation evidence and empirical application confirm efficiency gains achieved by regression adjustments relative to both the estimator without adjustment and the standard two-stage least squares estimator.

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Quantile‐Based Test for Heterogeneous Treatment Effects

Chung,

Olivares

2024

J of Applied Econometrics

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We introduce a permutation test for heterogeneous treatment effects based on the quantile process. However, tests based on the quantile process often suffer from estimated nuisance parameters that jeopardize their validity, even in large samples. To overcome this problem, we use Khmaladze's martingale transformation. We show that the permutation test based on the transformed statistic controls size asymptotically. Numerical evidence asserts the good size and power performance of our test procedure compared to other popular quantile‐based tests. We discuss a fast implementation algorithm and illustrate our method using experimental data from a welfare reform.

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Quantile treatment effects and bootstrap inference under covariate‐adaptive randomization

Cited by 17 publications

References 33 publications

Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations

Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations

Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance

Quantile‐Based Test for Heterogeneous Treatment Effects

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