AI 中文总结
本文提出在潜变量存在下，利用代理变量识别全数据律的一般条件，并通过代理加权方案构建一致且多重稳健的M估计量，实现函数估计。
AI 中文摘要
我们陈述了在存在潜变量的情况下，全数据律被识别的一般条件，利用与未观测变量相关联的关键观测变量（“代理”）。这些假设扩展了文献中现有示例所使用的假设，这些示例在相对灵活的模型假设下恢复全数据律。我们首先描述与我们的假设兼容的图模型，然后考虑作为全数据律泛函的目标参数，开发出使用观测数据产生一致M估计量的估计方程。我们的方法通过基于代理的加权方案，将全数据估计方程中出现的未观测随机变量替换为观测变量。该策略可扩展以构造观测数据影响函数，从而得到具有多重稳健性和\\(\sqrt{n}\\)-一致性等理想性质的估计量，尽管干扰函数的收敛速度慢于参数速度。
英文摘要
We state general conditions under which the full-data law is identified in the presence of latent variables, leveraging key observed variables ("proxies") associated with unobserved variables. These assumptions extend those used in existing examples from the literature that recover the full-data law under relatively flexible model assumptions. We first describe graphical models compatible with our assumptions, and then consider target parameters that are functionals of the full-data law, developing estimating equations that give rise to consistent M-estimators using the observed data. Our approach replaces unobserved random variables appearing in full-data estimating equations with observed variables via a proxy-based weighting scheme. This strategy can be extended to construct observed-data influence functions, giving estimators with desirable properties such as multiple robustness and \(\sqrt{n}\)-consistency despite slower than parametric convergence of nuisance functions.
