Optimized Variance Estimation under Interference and Complex Experimental Designs

• 成果类型: Article; Early Access
• 署名作者: Harshaw, Christopher; Middleton, Joel; Savje, Fredrik
• 署名单位: Columbia University; Uppsala University; Uppsala University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2627027
• 发表日期: 2026-05-12
• 关键词: Causal Inference; randomized experiments; variance estimation; Causal Inference; identification

摘要

Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and complex experimental designs. Experimenters must accept conservative variance estimators in these settings, but they can strive to minimize the conservativeness. In this article, we show that the task of constructing a minimally conservative variance estimator can be interpreted as an optimization problem that aims to find the lowest estimable upper bound of the true variance given the experimenter's risk preferences and knowledge of the potential outcomes. We characterize the set of admissible bounds in the class of quadratic forms, and we demonstrate that the optimization problem is a convex program for many natural objectives. The resulting variance estimators are guaranteed to be conservative regardless of whether the background knowledge used to construct the bound is correct, but the estimators are less conservative if the provided information is reasonably accurate. Numerical results show that the resulting variance estimators can be considerably less conservative than existing estimators, allowing experimenters to draw more informative inferences about treatment effects. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.