  We present a new experimental design procedure that divides a set of
experimental units into two groups in order to minimize error in estimating an
additive treatment effect. One concern is minimizing error at the experimental
design stage is large covariate imbalance between the two groups. Another
concern is robustness of design to misspecification in response models. We
address both concerns in our proposed design: we first place subjects into
pairs using optimal nonbipartite matching, making our estimator robust to
complicated non-linear response models. Our innovation is to keep the matched
pairs extant, take differences of the covariate values within each matched pair
and then we use the greedy switching heuristic of Krieger et al. (2019) or
rerandomization on these differences. This latter step greatly reduce covariate
imbalance to the rate $O_p(n^{-4})$ in the case of one covariate that are
uniformly distributed. This rate benefits from the greedy switching heuristic
which is $O_p(n^{-3})$ and the rate of matching which is $O_p(n^{-1})$.
Further, our resultant designs are shown to be as random as matching which is
robust to unobserved covariates. When compared to previous designs, our
approach exhibits significant improvement in the mean squared error of the
treatment effect estimator when the response model is nonlinear and performs at
least as well when it the response model is linear. Our design procedure is
found as a method in the open source R package available on CRAN called
GreedyExperimentalDesign.
