Sharp variance estimator and causal bootstrap in stratified randomized experiments
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911695031500800 |
|---|---|
| author | Yu, Haoyang Zhu, Ke Liu, Hanzhong |
| author_facet | Yu, Haoyang Zhu, Ke Liu, Hanzhong |
| contents | Randomized experiments are the gold standard for estimating treatment effects, and randomization serves as a reasoned basis for inference. In widely used stratified randomized experiments, randomization-based finite-population asymptotic theory enables valid inference for the average treatment effect, relying on normal approximation and a Neyman-type conservative variance estimator. However, when the sample size is small or the outcomes are skewed, the Neyman-type variance estimator may become overly conservative, and the normal approximation can fail. To address these issues, we propose a sharp variance estimator and two causal bootstrap methods to more accurately approximate the sampling distribution of the weighted difference-in-means estimator in stratified randomized experiments. The first causal bootstrap procedure is based on rank-preserving imputation and we prove its second-order refinement over normal approximation. The second causal bootstrap procedure is based on constant-treatment-effect imputation and is further applicable in paired experiments. In contrast to traditional bootstrap methods, where randomness originates from hypothetical super-population sampling, our analysis for the proposed causal bootstrap is randomization-based, relying solely on the randomness of treatment assignment in randomized experiments. Numerical studies and two real data applications demonstrate advantages of our proposed methods in finite samples. The \texttt{R} package \texttt{CausalBootstrap} implementing our method is publicly available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp variance estimator and causal bootstrap in stratified randomized experiments Yu, Haoyang Zhu, Ke Liu, Hanzhong Statistics Theory Applications Methodology Randomized experiments are the gold standard for estimating treatment effects, and randomization serves as a reasoned basis for inference. In widely used stratified randomized experiments, randomization-based finite-population asymptotic theory enables valid inference for the average treatment effect, relying on normal approximation and a Neyman-type conservative variance estimator. However, when the sample size is small or the outcomes are skewed, the Neyman-type variance estimator may become overly conservative, and the normal approximation can fail. To address these issues, we propose a sharp variance estimator and two causal bootstrap methods to more accurately approximate the sampling distribution of the weighted difference-in-means estimator in stratified randomized experiments. The first causal bootstrap procedure is based on rank-preserving imputation and we prove its second-order refinement over normal approximation. The second causal bootstrap procedure is based on constant-treatment-effect imputation and is further applicable in paired experiments. In contrast to traditional bootstrap methods, where randomness originates from hypothetical super-population sampling, our analysis for the proposed causal bootstrap is randomization-based, relying solely on the randomness of treatment assignment in randomized experiments. Numerical studies and two real data applications demonstrate advantages of our proposed methods in finite samples. The \texttt{R} package \texttt{CausalBootstrap} implementing our method is publicly available. |
| title | Sharp variance estimator and causal bootstrap in stratified randomized experiments |
| topic | Statistics Theory Applications Methodology |
| url | https://arxiv.org/abs/2401.16667 |