In clinical trials and causal inference, it is often critical to balance treatment allocation over influential covariates. In big data era, the number of covariates is usually very large, among which only a small fraction of them are influential to the response variable, due to sparsity. However, existed studies assume that all influential covariates are known, fixed and given. In this talk, we propose a procedure that can select the influential covariates from a diverging number of candidates and keep the allocation balanced among the important covariates, simultaneously. Under mild regulatory conditions, we show that the proposed procedure can pick out important covariates and balance treatment allocation among the important covariates consistently. Further, balancing treatment allocation can help the selection of important covariate, while picking out important covariates can help the randomization more efficient. Numerical studies support our theoretical discoveries for the proposed procedure. We also apply our method on a virtual re-design dataset of advertising vehicle choosing and show the advantages of the proposed procedure.
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