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

TL;DR

This paper extends the delta method for finite populations, enabling new asymptotic inference tools for causal estimators, including a finite population distribution for a causal ratio estimator.

Contribution

It develops a generalized delta method framework for finite populations, providing new asymptotic results and variance formulas for causal inference estimators.

Findings

Finite population asymptotic distribution for a causal ratio estimator.

New variance expressions for causal estimators.

Enhanced inference methods for finite population causal analysis.

Abstract

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.