Influence function (IF)-based estimators are widely used in mediation analysis due to their modeling flexibility, but standard implementations require direct estimation of the distribution functions of the mediator and treatment variables. Since these functions appear in the denominator of IF-based estimators, they can induce significant instability, particularly with continuous mediators. In this work, we propose an alternative implementation of IF-based estimators for both single- and multiple-mediator settings, based on reparametrizations of the likelihood. The key idea is to estimate the involved nuisance functions according to their role in the bias structure of the IF-based estimators. In our approach, key nuisance functions that are potential sources of instability are estimated using a novel nonparametric weighted balancing method-which can be viewed as a nonparametric extension of covariate balancing generalized to mediation analysis-fully stabilizing the estimators. We establish consistency and multiple robustness under suitable regularity conditions, and asymptotic normality. Simulation studies demonstrate substantial reductions in bias and variance relative to existing methods for continuous mediators. We further illustrate the approach using NHANES 2013-2014 data to estimate the effect of obesity on coronary heart disease mediated by Glycohemoglobin.

翻译：影响函数（IF）基估计器因其建模灵活性在中介分析中广泛应用，但标准实现方案要求直接估计中介变量和处理变量的分布函数。由于这些函数出现在IF基估计器的分母中，它们可能引发显著的不稳定性，特别是在连续中介变量的情况下。本研究基于似然函数的重新参数化，提出了适用于单中介变量与多中介变量场景的IF基估计器替代实现方案。核心思想是根据各干扰函数在IF基估计器偏置结构中的作用进行估计。在我们的方法中，将可能导致不稳定的关键干扰函数通过一种新颖的非参数加权平衡方法进行估计——该方法可视为协变量平衡在中介分析中的非参数扩展——从而完全稳定了估计器。我们在适当正则条件下建立了估计量的一致性与多重稳健性，以及渐近正态性。仿真研究表明，相较于现有连续中介变量处理方法，本方法能显著降低偏置与方差。我们进一步通过NHANES 2013-2014数据，应用该方法估计了肥胖通过糖化血红蛋白中介对冠心病的影响效应。