Jinglong Zhao
arXiv 15 Aug 2026 · Econometrics
arXiv:2608.15333 · PDF · Extracted main text
We propose a family of control variate estimators for variance reduction in design-based survey sampling and causal inference, with and without interference. In these settings, inverse probability weighting (IPW) estimators are widely used, but may have large variance when sampling, treatment, or exposure probabilities are small. Building on the observation that several common estimators, including the Hajek, normalized, and augmented inverse probability weighting (AIPW) estimators, correct the Horvitz-Thompson estimator by canceling part of its randomness, we provide a unified interpretation of these estimators as special cases of a general control variate estimator. We then construct optimal control variates that can further reduce the finite sample variance compared to these common estimators. We parameterize the proposed control variates by their bases and characterize the optimal bases through a stochastic optimization formulation. In survey sampling and causal inference without interference, the optimal bases are characterized by leading eigenvectors of matrices that depend on both the design-based sampling structure and the model-based outcome uncertainty. In causal inference under network interference, the optimal bases solve a nonconvex quadratic optimization problem; we provide a $\frac{1}{2}$-approximate solution and an alternating local search heuristic. We apply the control variate estimators to the Swiss Environmental Panel survey data and the Chinese social network data, and conduct extensive simulations to show that the proposed control variate estimators can achieve substantial variance reduction.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cai J, Janvry AD, Sadoulet E (2015) Social networks and the decision to insure | 1.000 | 10 | 3 | 100% |
| 2 | Quo F, Rudolph L, Gomm S, Wehrli S, Bernauer T (2021) Swiss environmental panel study 2018-2021, wave 1-6, cumulative data | 1.000 | 5 | 3 | 100% |
| 3 | Ross N (2011) Fundamentals of stein’s method | 0.928 | 4 | 4 | 100% |
| 4 | Fan K (1949) On a theorem of weyl concerning eigenvalues of linear transformations i | 0.874 | 6 | 2 | 100% |
| 5 | Zhao J (2024) Experimental design for causal inference through an optimization lens | 0.843 | 3 | 3 | 100% |
| 6 | Aronow PM, Samii C (2017) Estimating average causal effects under general interference, with application to a social network experiment | 0.811 | 4 | 2 | 100% |
| 7 | Khan S, Ugander J (2023) Adaptive normalization for ipw estimation | 0.811 | 4 | 2 | 100% |
| 8 | Horn RA, Johnson CR (2012) Matrix analysis | 0.737 | 3 | 2 | 100% |
| 9 | Robins JM, Rotnitzky A, Zhao LP (1994) Estimation of regression coefficients when some regressors are not always observed | 0.737 | 3 | 2 | 100% |
| 10 | Särndal CE, Thomsen I, Hoem JM, Lindley D, Barndorff-Nielsen O, Dale… (1978) Design-based and model-based inference in survey sampling [with discussion and reply] | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 67 scored citations.