Designing experiments for causal effect estimation remains an enduring topic in both machine learning and statistics. While much of the existing statistical literature focuses on using central limit theorems to analyze asymptotic properties of estimators, a parallel line of research has emerged around theoretical tools that provide finite-sample error bounds, offering performance on par with—or superior to—the asymptotic approaches. These finite-sample results are especially relevant in active sampling settings where the sample size is limited (for instance, under privacy or cost constraints). In this paper, we develop a finite-sample estimator with sample complexity analysis and extend its applicability to social networks. Through simulations and real-world experiments, we show that our method achieves higher estimation accuracy with fewer samples than traditional estimators endowed with asymptotic normality and other estimators backed by finite-sample guarantees.

Active Treatment Effect Estimation via Limited Samples