``Low-rank Covariate Balancing Estimators under Interference.''

 

  Abstract

A key methodological challenge in observational studies with interference between units is twofold: (1) each unit's outcome may depend on many others' treatments, and (2) treatment assignments may exhibit complex dependencies across units. We develop a general statistical framework for constructing robust causal effect estimators to address these challenges. We first show that, without restricting the patterns of interference, the standard inverse probability weighting (IPW) estimator is the only uniformly unbiased estimator when the propensity score is known. In contrast, no estimator has such a property if the propensity score is unknown. We then introduce a low-rank structure of potential outcomes as a broad class of structural assumptions about interference. This framework encompasses common assumptions such as anonymous, nearest-neighbor, and additive interference, while flexibly allowing for more complex study-specific interference assumptions. Under this low-rank assumption, we show how to construct an unbiased weighting estimator for a large class of causal estimands. The proposed weighting estimator does not require knowledge of true propensity scores and is therefore robust to unknown treatment assignment dependencies that often exist in observational studies. If the true propensity score is known, we can obtain an unbiased estimator that is more efficient than the IPW estimator by leveraging a low-rank structure. We establish the finite sample and asymptotic properties of the proposed weighting estimator, develop a data-driven procedure to select among candidate low-rank structures, and validate our approach through simulation and empirical studies.

  Related Papers

Imai, Kosuke and Marc Ratkovic. (2014). ``Covariate Balancing Propensity Score.'' Journal of the Royal Statistical Society, Series B (Statistical Methodology), Vol. 76, No. 1 (January), pp. 243-263.
Imai, Kosuke and Marc Ratkovic. (2015). ``Robust Estimation of Inverse Probability Weights for Marginal Structural Models.'' Journal of the American Statistical Association, Vol. 110, No. 511 (September), pp. 1013-1023. (lead article)
Fong, Christian, Chad Hazlett, and Kosuke Imai. (2018). ``Covariate Balancing Propensity Score for a Continuous Treatment: Application to the Efficacy of Political Advertisements.'' Annals of Applied Statistics, Vol. 12, No. 1, pp. 156-177.
Ning, Yang, Sida Peng, and Kosuke Imai. (2020). ``Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score..'' Biometrika, Vol. 107, No. 3 (September), pp. 533-554.
Fan, Jianqing, Kosuke Imai, Inbeom Lee, Han Liu, Yang Ning, and Xiaolin Yang. (2023). ``Optimal Covariate Balancing Conditions in Propensity Score Estimation.'' Journal of Business & Economic Statistics, Vol. 41, No. 1, pp. 97-110.

© Kosuke Imai
 Last modified: Thu Dec 18 08:08:56 EST 2025