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Abstract:
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In observational studies, sample surveys, and regression settings, weighting methods are widely used to adjust for or balance observed covariates. Recently, many methods have been proposed that instead focus on directly balancing the covariates while minimizing the dispersion of the weights. In this paper, we call this general class of weights minimal approximately balancing weights (MABW) and study their properties by establishing a connection with shrinkage estimation of the propensity score. This connection allows us to characterize the asymptotic properties of MABW by building on the large sample results from propensity score estimation. In particular, we show that, under standard technical conditions, MABW are consistent estimates of the true inverse probability weights. We also show that the resulting weighting estimator is consistent, asymptotically normal, and semiparametrically efficient. For applications, we present a finite sample oracle inequality that shows the loss incurred by balancing too many functions of the covariates is limited in MABW. We also provide an algorithm for choosing the degree of approximate balancing in MABW. We conclude with numerical results.
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