Design-Based Theory for Lasso Adjustment in Randomized Block Experiments and Rerandomized Experiments
针对随机区组实验中的高维协变量，提出基于Lasso的回归调整方法，证明其渐近性质并给出保守方差估计，适用于区组数、大小趋于无穷及异质性处理效应场景。
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.