Missing data is an universal problem in statistics. We develop a unified framework for estimating parameters defined by general estimating equations under a missing-at-random (MAR) mechanism, based on generalized entropy calibration weighting. We construct weights by minimizing a convex entropy subject to (i) balancing constraints on a data-adaptive calibration function, estimated using flexible machine-learning predictors with cross-fitting, and (ii) a debiasing constraint involving the fitted propensity score (PS) model. The resulting estimator is doubly robust, remaining consistent if either the outcome regression (OR) or the PS model is correctly specified, and attains the semiparametric efficiency bound when both models are correctly specified. Our formulation encompasses classical inverse probability weighting (IPW) and augmented IPW (AIPW) as special cases and accommodates a broad class of entropy functions. We illustrate the versatility of the approach in three important settings: semi-supervised learning with unlabeled outcomes, regression analysis with missing covariates, and causal effect estimation in observational studies. Extensive simulation studies and real-data applications demonstrate that the proposed estimators achieve greater efficiency and numerical stability than existing methods. In particular, the proposed estimator outperforms the classical AIPW estimator under the OR model misspecification.

翻译：缺失数据是统计学中的普遍问题。本文基于广义熵校准加权，开发了一个统一框架，用于在随机缺失机制下通过一般估计方程估计参数。我们通过最小化凸熵来构建权重，该过程需满足两个约束条件：(i) 基于数据自适应校准函数的平衡约束（该函数通过交叉拟合的灵活机器学习预测器进行估计），(ii) 涉及已拟合倾向得分模型的去偏约束。所得估计量具有双重稳健性：当结果回归模型或倾向得分模型之一设定正确时保持一致性，当两个模型均正确设定时可达到半参数效率界。我们的框架将经典逆概率加权和增强逆概率加权作为特例包含在内，并能容纳一大类熵函数。我们通过三个重要场景展示了该方法的普适性：无标记结果的半监督学习、含缺失协变量的回归分析，以及观察性研究中的因果效应估计。大量模拟研究和实际数据应用表明，所提出的估计量比现有方法具有更高的效率和数值稳定性。特别地，在结果回归模型误设的情况下，所提出的估计量优于经典的增强逆概率加权估计量。