  Mahalanobis distance between treatment group and control group covariate
means is often adopted as a balance criterion when implementing a
rerandomization strategy. However, this criterion may not work well for
high-dimensional cases because it balances all orthogonalized covariates
equally. Here, we propose leveraging principal component analysis (PCA) to
identify proper subspaces in which Mahalanobis distance should be calculated.
Not only can PCA effectively reduce the dimensionality for high-dimensional
cases while capturing most of the information in the covariates, but it also
provides computational simplicity by focusing on the top orthogonal components.
We show that our PCA rerandomization scheme has desirable theoretical
properties on balancing covariates and thereby on improving the estimation of
average treatment effects. We also show that this conclusion is supported by
numerical studies using both simulated and real examples.
