Semiparametric estimation of treatment effect with density ratio model

In this study we propose a unified semiparametric approach to estimate various indices of treatment effect under the density ratio model, which connects two density functions by an exponential tilt. For each index, we construct two estimating functions based on the model and apply the generalized method of moments to improve the estimates. The estimating functions are allowed to be non smooth with respect to parameters and hence make the proposed method more flexible. We establish the asymptotic properties of the proposed estimators and illustrate the application with several simulations and two real data sets.