  Controlled experiments are widely used in many applications to investigate
the causal relationship between input factors and experimental outcomes. A
completely randomized design is usually used to randomly assign treatment
levels to experimental units. When covariates of the experimental units are
available, the experimental design should achieve covariate balancing among the
treatment groups, such that the statistical inference of the treatment effects
is not confounded with any possible effects of covariates. However, covariate
imbalance often exists, because the experiment is carried out based on a single
realization of the complete randomization. It is more likely to occur and
worsen when the size of the experimental units is small or moderate. In this
paper, we introduce a new covariate balancing criterion, which measures the
differences between kernel density estimates of the covariates of treatment
groups. To achieve covariate balance before the treatments are randomly
assigned, we partition the experimental units by minimizing the criterion, then
randomly assign the treatment levels to the partitioned groups. Through
numerical examples, we show that the proposed partition approach can improve
the accuracy of the difference-in-mean estimator and outperforms the complete
randomization and rerandomization approaches.
