Central limit theorems via Stein's method for randomized experiments under interference

TL;DR

This paper establishes conditions under which treatment effect estimators remain asymptotically normal in randomized experiments with interference, using Stein's method to handle complex dependency structures and providing robust inference tools.

Contribution

It introduces a central limit theorem for treatment estimators under interference, extending classical results to settings with dependent units via Stein's method.

Findings

Horvitz-Thompson estimator is asymptotically normal under restricted interference.

A CLT for difference-in-means estimator with widespread interference.

Proposes a conservative variance estimator accounting for interference.

Abstract

We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson estimator is asymptotically normal under a restricted interference condition characterized by limiting the degree of the dependency graph. The amount of interference is allowed to grow with the population size. We then provide a central limit theorem for the difference-in-means estimator that can handle interference that exists between all pairs of units, provided most of the interference is captured by a restricted-degree dependency graph. The asymptotic variance admits a decomposition into two terms: (a) the variance that is expected under no-interference and (b) the additional variance contributed by interference. We propose a conservative variance estimator based on this variance decomposition. The results arise as an application of Stein's method. For practitioners, our results show that standard estimators continue to exhibit normality in large sample sizes and that inference can be made robust to mild forms of interference.