Design-based theory for Lasso adjustment in randomized block experiments and rerandomized experiments

Abstract

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. This study proposes a regression adjustment method based on the least absolute shrinkage and selection operator (Lasso) to efficiently estimate the average treatment effect in randomized block experiments with high-dimensional covariates. We derive the asymptotic properties of the proposed estimator and outline the conditions under which this estimator is more efficient than the unadjusted one. We provide a conservative variance estimator to facilitate valid inferences. Our framework allows one treated or control unit in some blocks and heterogeneous propensity scores across blocks, thus including paired experiments and finely stratified experiments as special cases. We further accommodate rerandomized experiments and a combination of blocking and rerandomization. Moreover, our analysis allows both the number of blocks and block sizes to tend to infinity, as well as heterogeneous treatment effects across blocks without assuming a true outcome data-generating model. Simulation studies and two real-data analyses demonstrate the advantages of the proposed method.

References in corpus (14)

• On asymptotically optimal confidence regions and tests for high-dimensional models
• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
• Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique
• Rerandomization to improve covariate balance in experiments
• Deep Neural Networks for Estimation and Inference
• Lasso adjustments of treatment effect estimates in randomized experiments
• Randomization Does Not Justify Logistic Regression
• High-dimensional regression adjustments in randomized experiments
• Regression adjustment in completely randomized experiments with a diverging number of covariates
• Regression analysis for covariate-adaptive randomization: A robust and efficient inference perspective
• A general theory of regression adjustment for covariate-adaptive randomization: OLS, Lasso, and beyond
• Insights on Variance Estimation for Blocked and Matched Pairs Designs
• Rerandomization in stratified randomized experiments
• Blocking estimators and inference under the Neyman-Rubin model