Unbiased Regression-Adjusted Estimation of Average Treatment Effects in Randomized Controlled Trials

This article introduces a leave-one-out regression adjustment estimator (LOORA) for estimating average treatment effects in randomized controlled trials. The method removes the finite-sample bias of conventional regression adjustment and provides exact variance expressions for LOORA versions of the Horvitz-Thompson and difference-in-means estimators under simple and complete random assignment. Ridge regularization limits the influence of high-leverage observations, improving stability and precision in small samples. In large samples, LOORA attains the asymptotic efficiency of regression-adjusted estimator as characterized by Lin (2013, Annals of Applied Statistics), while remaining exactly unbiased. To construct confidence intervals, we rely on asymptotic variance estimates that treat the estimator as a two-step procedure, accounting for both the regression adjustment and the random assignment stages. Two within-subject experimental applications that provide realistic joint distributions of potential outcomes as ground truth show that LOORA eliminates substantial biases and achieves close-to-nominal confidence interval coverage.