  Empirical regression discontinuity (RD) studies often use covariates to
increase the precision of their estimates. In this paper, we propose a novel
class of estimators that use such covariate information more efficiently than
existing methods and can accommodate many covariates. It involves running a
standard RD analysis in which a function of the covariates has been subtracted
from the original outcome variable. We characterize the function that leads to
the estimator with the smallest asymptotic variance, and consider feasible
versions of such estimators in which this function is estimated, for example,
through modern machine learning techniques.
