AI 中文总结
研究离散选择模型中反事实选择概率的识别问题，通过将其表示为混合分布的线性泛函，刻画识别集并对其端点推断，给出相关条件及算法，证明插件端点估计量渐近正态性并建立局部收敛保证。
AI 中文摘要
在离散选择模型中，针对有限选择集观测到的选择概率可能无法识别未观测到的选择集下的反事实选择概率。我们将此反事实概率表示为混合分布的线性泛函。由于目标是分布的泛函且其支撑不限于有限集，参数空间是无限维的，而数据仅施加有限多个矩限制，所以观测到的选择概率不一定能点识别这样的目标。识别集被定义为与观测到的选择概率兼容的目标值集。我们不是施加条件以确保点识别，而是刻画识别集，并对其上下端点进行推断。我们将每个端点表示为概率测度上线性规划的值，并给出获得识别界路径可微性的条件。结果，我们能够证明插件端点估计量的渐近正态性。最后，我们提供一种类似期望最大化的算法来验证候选值在识别集中的成员资格，并建立局部收敛保证。
英文摘要
In a discrete choice model, choice probabilities observed for a finite collection of choice sets may not identify a counterfactual choice probability under an unobserved choice set. We represent this counterfactual probability as a linear functional of a mixing distribution. Because the target is a functional of a distribution whose support is not restricted to a finite set, the parameter space is infinite-dimensional, while the data impose only finitely many moment restrictions. Therefore, observed choice probabilities need not point identify such a target. The identified set is defined as the set of target values compatible with observed choice probabilities. Rather than imposing conditions to ensure point identification, we characterize the identified set, and conduct inference on its lower and upper endpoints. We represent each endpoint as the value of a linear program over probability measures, and give conditions to obtain pathwise differentiability of the identification bounds. As a consequence, we are able to prove asymptotic normality of plug-in endpoint estimators. Finally, we provide an Expectation-Maximization-like algorithm for certifying membership of candidate values in the identified set and establish local convergence guarantees.
CommentsAntoine Scheid and Jia Wan were equal contributors to this work
