Estimation of mean response via effective balancing score

We introduce effective balancing scores for estimation of the mean response under a missing at random mechanism. Unlike conventional balancing scores, the effective balancing scores are constructed via dimension reduction free of model specification. Three types of effective balancing scores are introduced: those that carry the covariate information about the missingness, the response, or both. They lead to consistent estimation with little or no loss in efficiency. Compared to existing estimators, the effective balancing score based estimator relieves the burden of model specification and is the most robust. It is a near-automatic procedure which is most appealing when high dimensional covariates are involved. We investigate both the asymptotic and the numerical properties, and demonstrate the proposed method in a study on Human Immunodeficiency Virus disease.