Covariate Balancing Based on Kernel Density Estimates for Controlled Experiments
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Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes. Completely random design is usually used to randomly assign treatment levels to test units. When covariates of the test units are available, the experimental design should achieve covariate balancing between 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. The issue becomes worse when the size of the test 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 balancing before the treatments are randomly assigned, we partition the test 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. It outperforms the complete randomization and rerandomization approaches.
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