发表机构
Harvard University（哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对不完美测量下的部分识别问题，提出基于分布鲁棒优化的通用框架，通过构建基准分布邻域计算并收紧参数界限，无需额外数据或假设，适用于网络、缺失结果和回归等场景。
AI 中文摘要
不完美的测量允许不同的潜在分布生成相同的观测数据。连接未观测成分的限制条件可能使得刻画所有兼容分布并计算由此产生的参数值范围变得困难。我们探讨如何在不增加额外数据或更强假设的情况下，构建可计算的参数界限并使其更紧。我们基于分布鲁棒优化，开发了一个在不完美测量下进行部分识别的通用框架。我们利用测量限制条件在基准分布周围构建一个邻域，确保所有兼容分布都位于该邻域内。通过在该邻域上进行优化，可以通过一个可适应不同测量问题的通用程序获得参数界限。基准分布的选择会影响这些界限的信息量。我们建立了条件，在这些条件下，更换基准分布可以收紧界限，同时保留与相同数据和假设一致的所有参数值。在网络、缺失结果和回归中的应用展示了该框架如何收紧界限，并能够恢复完整的兼容值范围。
英文摘要
Imperfect measurements allow different underlying distributions to generate the same observations. Restrictions linking unobserved components can make it difficult to characterize all compatible distributions and compute the resulting range of parameter values. We ask how to construct computable parameter bounds and tighten them without additional data or stronger assumptions. We develop a general framework for partial identification under imperfect measurement based on distributionally robust optimization. We use measurement restrictions to construct a neighborhood around a benchmark distribution, ensuring that every compatible distribution lies within it. Optimizing over this neighborhood gives parameter bounds through a common procedure that can be adapted to different measurement problems. The choice of benchmark affects how informative these bounds are. We establish conditions under which changing it can tighten the bounds while preserving every parameter value consistent with the same data and assumptions. Applications to networks, missing outcomes, and regression illustrate how the framework tightens bounds and can recover the full range of compatible values.
Comments62 pages, 4 figures
