调查抽样与因果推断的最优控制变量
Optimal Control Variates for Survey Sampling and Causal Inference
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中文总结 AI 辅助
本文针对调查抽样与因果推断场景提出一类最优控制变量估计量，通过参数化基函数并求解对应优化问题，在真实调查数据和模拟中实现了显著的方差缩减。
中文摘要 AI 辅助
我们提出了一类控制变量估计量，用于基于设计的调查抽样和因果推断（含干扰与无干扰情形）中的方差缩减。在这些场景中，逆概率加权（IPW）估计量被广泛应用，但当抽样、处理或暴露概率较小时，其方差可能较大。基于以下观察：包括Hajek估计量、归一化估计量及增广逆概率加权（AIPW）估计量在内的若干常用估计量，通过抵消Horvitz-Thompson估计量的部分随机性对其进行校正，我们将这些估计量统一解释为通用控制变量估计量的特例。随后，我们构造最优控制变量，与上述常用估计量相比，其可进一步缩减有限样本方差。我们通过基函数对所提控制变量进行参数化，并通过随机优化公式刻画最优基函数。在无干扰的调查抽样与因果推断中，最优基函数由依赖于基于设计的抽样结构和基于模型的结果不确定性的矩阵的主特征向量刻画；在网络干扰下的因果推断中，最优基函数需求解非凸二次优化问题，我们提供了1/2近似解和交替局部搜索启发式算法。我们将该控制变量估计量应用于瑞士环境面板调查数据和中国社交网络数据，并开展大量模拟实验，结果表明所提控制变量估计量可实现显著的方差缩减。
英文摘要
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 estimator, the normalized estimator, the augmented inverse probability weighting (AIPW) estimator, and the targeted maximum likelihood estimator (TMLE), all 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 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.
