Design-based theory for Lasso adjustment in randomized block experiments with a general blocking scheme

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. Regression adjustment is highly encouraged in the analysis stage to adjust for the remaining covariate imbalances. This study proposes methods that combine blocking, rerandomization, and regression adjustment techniques in randomized experiments with high-dimensional covariates and a general blocking scheme. In the design stage, we suggest the implementation of blocking and rerandomization to balance the fixed number of covariates most relevant to the outcomes. For the analysis stage, we propose a regression adjustment method based on least absolute shrinkage and selection operator (Lasso) to adjust for the remaining imbalances in additional 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. Moreover, we provide a conservative variance estimator to facilitate valid inferences. Our design-based analysis allows for model misspecification and is applicable to heterogeneous block sizes, propensity scores, and treatment effects. Simulation studies and two real-data analyses demonstrate the advantages of the proposed method.