  Stratification and rerandomization are two well-known methods used in
randomized experiments for balancing the baseline covariates. Renowned scholars
in experimental design have recommended combining these two methods; however,
limited studies have addressed the statistical properties of this combination.
This paper proposes two rerandomization methods to be used in stratified
randomized experiments, based on the overall and stratum-specific Mahalanobis
distances. The first method is applicable for nearly arbitrary numbers of
strata, strata sizes, and stratum-specific proportions of the treated units.
The second method, which is generally more efficient than the first method, is
suitable for situations in which the number of strata is fixed with their sizes
tending to infinity. Under the randomization inference framework, we obtain the
asymptotic distributions of estimators used in these methods and the formulas
of variance reduction when compared to stratified randomization. Our analysis
does not require any modeling assumption regarding the potential outcomes.
Moreover, we provide asymptotically conservative variance estimators and
confidence intervals for the average treatment effect. The advantages of the
proposed methods are exhibited through an extensive simulation study and a
real-data example.
