发表机构
University of Michigan; Emory University（密歇根大学; 埃默里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将部分识别问题转化为路径空间上的熵正则化最优传输问题，通过Sinkhorn迭代高效求解，并建立收敛性与渐近性质，适用于工具变量和异质需求模型。
AI 中文摘要
在许多统计设定中，现有数据和所维持的假设不足以唯一识别感兴趣的模型参数。在这种情况下，人们只能识别保证包含真实参数的集合。这些集合通常通过线性规划来刻画，该规划在与观测数据兼容的模型上进行优化。这些规划在优化变量和约束数量上可能是无限维的。我们提供了一种统一的方法来刻画和求解此类优化问题，将其表述为路径空间上的最优传输问题。这使得我们能够通过熵惩罚对问题进行正则化，将其重新表述为多边际熵正则化最优传输问题，并可通过Sinkhorn迭代高效求解。此外，这使我们能够建立正则化值向最紧边界的收敛性，推导出插件估计量的一致性速率，并获得近似边界的渐近分布。该方法具有通用性，适用于从具有连续变量的工具变量模型到异质需求模型中的福利估计等各种设定。我们在模拟中验证了统计和计算性质，并将其应用于需求估计。
英文摘要
In many statistical settings, the available data and maintained assumptions do not suffice to uniquely identify the model parameters of interest. In such cases, one can only identify sets which are guaranteed to contain the true parameters. These are often characterized through linear programs that optimize over models compatible with the observed data. These programs can be infinite-dimensional in the optimizer and the number of constraints. We provide a unified way to characterize and solve such optimization problems by phrasing them as optimal transport problems on path spaces. This allows us to regularize the problem with an entropy penalty, recasting it as a multi-marginal entropic optimal transport problem, which can be solved efficiently via Sinkhorn iterations. In addition, it allows us to establish convergence of the regularized value to the sharpest bound, derive consistency rates for a plug-in estimator, and obtain asymptotic distribution for approximate bounds. The method is general and accommodates settings ranging from instrumental variable models with continuous variables to welfare estimation in heterogeneous demand models. We verify the statistical and computational properties in simulations and provide an application to demand estimation.
