Note on the Delta Method for Finite Population Inference with Applications to Causal Inference

The delta method creates more general inference results when coupled with central limit theorem results for the finite population. This opens up a range of new estimators for which we can find finite population asymptotic properties. We focus on the use of this method to derive asymptotic distributional results and variance expressions for causal estimators. We illustrate the use of the method by obtaining a finite population asymptotic distribution for a causal ratio estimator.