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

TL;DR

This paper introduces a Lasso-based regression adjustment method for randomized block and rerandomized experiments, improving the estimation of treatment effects with high-dimensional covariates and complex experimental designs.

Contribution

It develops a novel Lasso adjustment framework that handles high-dimensional covariates, heterogeneous treatment effects, and various experimental designs including rerandomization.

Findings

The proposed estimator is asymptotically more efficient than unadjusted estimates under certain conditions.

A conservative variance estimator enables valid inference in complex experimental settings.

Simulation and real-data analyses demonstrate the method's practical advantages.

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.