Session I (May 15, 8:30am-10:00am): Causal Inference and Experimental Design, organized by Tirthankar Dasgupta

• Title: Kernel Discrepancy-Based Rerandomization for Controlled Experiments 

• Speaker: Lulu Kang, University of MA, Amherst

• Abstract: Controlled experiments have been widely used in various disciplines for causal inference. Rerandomization has been proposed and advocated to improve the covariates balance. One key component in rerandomization is the balance criterion. In this article, we introduce the kernel discrepancy between the empirical distributions of the covariates in different treatment groups and show that it the upper bound of the variance of difference-in-mean estimator of the treatment effects. Accordingly, we propose using kernel discrepancy as a balance criterion. Using linear kernel function, we obtain the distribution of the kernel discrepancy for finite samples, which provides the critical value for an acceptable rerandomization. For more complicated kernel functions, we propose using empirical distributions of the kernel discrepancy to obtain the critical value. The kernel discrepancy has many merits. First, it is model-free and suitable to both continuous and categorical covariates data. Furthermore, the discrepancy-based criterion is model-free and thus makes the estimation of the treatment effect(s) robust to the model assumptions. More importantly, the proposed design is applicable to both continuous and categorical response measurements. Through simulation study and a real example, we show that the proposed design approach achieves accurate estimation even if the model assumption is not correct.