Reweighted nonparametric likelihood inference for linear functionals

This paper is concerned with inference on finite dimensional parameters in semiparametric moment condition models, where the moment functionals are linear with respect to unknown nuisance functions. By exploiting this linearity, we reformulate the inference problem via the Riesz representer, and develop a general inference procedure based on nonparametric likelihood. For treatment effect or missing data analysis, the Riesz representer is typically associated with the inverse propensity score even though the scope of our framework is much wider. In particular, we propose a two-step procedure, where the first step computes the projection weights to approximate the Riesz representer, and the second step re-weights the moment conditions so that the likelihood increment admits an asymptotically pivotal chi-square calibration. Our re-weighting method is naturally extended to inference on treatment effects and data combination models, and other semiparametric problems. Simulation and empirical examples illustrate usefulness of the proposed method.