Inference on High Dimensional Selective Labeling Models
高维选择性标签模型的统计推断AI 解读 ↓
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高维选择性标签模型的统计推断
- 研究问题
- 当二元结果只有在另一主体作出特定选择后才被观测时，如何处理内生样本选择，并在两条方程均含大量协变量时进行推断？
- 方法与思路
- 作者将半参数分批梯度下降与用于控制选择偏差的新排序算法结合，提出不指定分布的估计程序，并研究维度增长下的性质。
- 材料陈述的贡献
- 摘要称该程序适合多协变量环境，建立了两条方程维度增长时的渐近性质，并通过模拟与司法保释数据考察有限样本表现。
- 阅读关注点
- 应核对选择方程与结果方程的识别条件、排序如何控制选择偏差，以及维度增长限制、算法收敛和推断所需条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未列出识别假设及增长速率，不指定分布也不意味着无需其他限制。
原文摘要
A class of simultaneous equation models arise in the many domains where observed binary outcomes are themselves a consequence of the existing choices of of one of the agents in the model. These models are gaining increasing interest in the computer science and machine learning literatures where they refer the potentially endogenous sample selection as the {\em selective labels} problem. Empirical settings for such models arise in fields as diverse as criminal justice, health care, and insurance. For important recent work in this area, see for example Lakkaruju et al. (2017), Kleinberg et al. (2018), and Coston et al.(2021) where the authors focus on judicial bail decisions, and where one observes the outcome of whether a defendant filed to return for their court appearance only if the judge in the case decides to release the defendant on bail. Identifying and estimating such models can be computationally challenging for two reasons. One is the nonconcavity of the bivariate likelihood function, and the other is the large number of covariates in each equation. Despite these challenges, in this paper we propose a novel distribution free estimation procedure that is computationally friendly in many covariates settings. The new method combines the semiparametric batched gradient descent algorithm introduced in Khan et al.(2023) with a novel sorting algorithms incorporated to control for selection bias. Asymptotic properties of the new procedure are established under increasing dimension conditions in both equations, and its finite sample properties are explored through a simulation study and an application using judicial bail data.