Covariate balancing based on kernel density estimates for controlled experiments

Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes. A completely randomised 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 realisation of the complete randomisation. 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 minimising 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 randomisation and rerandomisation approaches.