Conditionally Affinely Invariant Rerandomization and its Admissibility

Rerandomization utilizes modern computing ability to search for covariate balance improved experimental design while adhering to the randomization principle originally advocated by RA Fisher. Conditionally affinely invariant rerandomization has the ``Equal Percent Variance Reducing'' property on subsets of conditionally ellipsoidally symmetric covariates. It is suitable to deal with covariates of varying importance or mixed types and usually produces multiple balance scores. ``Unified'' and `` intersection'' methods are common ways of deciding on multiple scores. In general, `` intersection'' methods are computationally more efficient but asymptotically inadmissible. As computational cost is not a major concern in experimental design, we recommend ``unified'' methods to build admissible criteria for rerandomization