  The propensity score analysis is one of the most widely used methods for
studying the causal treatment effect in observational studies. This paper
studies treatment effect estimation with the method of matching weights. This
method resembles propensity score matching but offers a number of new features
including efficient estimation, rigorous variance calculation, simple
asymptotics, statistical tests of balance, clearly identified target population
with optimal sampling property, and no need for choosing matching algorithm and
caliper size. In addition, we propose the mirror histogram as a useful tool for
graphically displaying balance. The method also shares some features of the
inverse probability weighting methods, but the computation remains stable when
the propensity scores approach 0 or 1. An augmented version of the matching
weight estimator is developed that has the double robust property, i.e., the
estimator is consistent if either the outcome model or the propensity score
model is correct. In the numerical studies, the proposed methods demonstrated
better performance than many widely used propensity score analysis methods such
as stratification by quintiles, matching with propensity scores, and inverse
probability weighting.
