  Rerandomization is a strategy of increasing efficiency as compared to
complete randomization. The idea with rerandomization is that of removing
allocations with imbalance in the observed covariates and then randomizing
within the set of allocations with balance in these covariates. Standard
asymptotic inference based on mean difference estimator is however conservative
after rerandomization. Given a Mahalanobis distance criterion for removing
imbalanced allocations, Li et al. (2018) derived the asymptotic distribution of
the mean difference estimator and suggested a consistent estimator of its
variance. This paper discusses several alternative methods of inference under
rerandomization, and compare their performance with that of the method in Li et
al. (2018) through a large Monte Carlo simulation. We conclude that some of the
methods work better for small or moderate sample sized experiments than the
method in Li et al. (2018).
