  Randomization ensures that observed and unobserved covariates are balanced,
on average. However, randomizing units to treatment and control often leads to
covariate imbalances in realization, and such imbalances can inflate the
variance of estimators of the treatment effect. One solution to this problem is
rerandomization---an experimental design strategy that randomizes units until
some balance criterion is fulfilled---which yields more precise estimators of
the treatment effect if covariates are correlated with the outcome. Most
rerandomization schemes in the literature utilize the Mahalanobis distance,
which may not be preferable when covariates are correlated or vary in
importance. As an alternative, we introduce an experimental design strategy
called ridge rerandomization, which utilizes a modified Mahalanobis distance
that addresses collinearities among covariates and automatically places a
hierarchy of importance on the covariates according to their eigenstructure.
This modified Mahalanobis distance has connections to principal components and
the Euclidean distance, and---to our knowledge---has remained unexplored. We
establish several theoretical properties of this modified Mahalanobis distance
and our ridge rerandomization scheme. These results guarantee that ridge
rerandomization is preferable over randomization and suggest when ridge
rerandomization is preferable over standard rerandomization schemes. We also
provide simulation evidence that suggests that ridge rerandomization is
particularly preferable over typical rerandomization schemes in
high-dimensional or high-collinearity settings.
