Subvector Inference in Partially Identified Models with Many Moment Inequalities
含大量矩不等式的部分识别模型中的子向量推断AI 解读 ↓
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含大量矩不等式的部分识别模型中的子向量推断
- 研究问题
- 在矩不等式数量随样本量快速增长的部分识别模型中，如何对处理效应或政策参数等子向量进行统一有效推断？
- 方法与思路
- 作者将原假设约束下对参数取最小、对矩条件取最大的统计量，与自助法或解析临界值比较，并设计数据驱动调参。
- 材料陈述的贡献
- 摘要称方法统一控制渐近检验水平并给出显式收敛率，无须依赖 Donsker 类弱收敛，另提供较保守但易实施的方案。
- 阅读关注点
- 应核对原假设参数集合的优化、矩条件数量增长限制、调参防止过度集中的机制，以及不同临界值方法的有效性条件。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及期刊接收未核实；摘要未列完整条件和计算方案，不能把渐近水平控制视为有限样本精确。
原文摘要
This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential rates. Our main motivating application is subvector inference, i.e., inference on a single component of the partially identified parameter vector associated with a treatment effect or a policy variable of interest. Our inference method compares a MinMax test statistic (minimum over parameters satisfying $H_0$ and maximum over moment inequalities) against critical values that are based on bootstrap approximations or analytical bounds. We show that this method controls asymptotic size uniformly over a large class of data generating processes despite the partially identified many moment inequality setting. The finite sample analysis allows us to obtain explicit rates of convergence on the size control. Our results are based on combining non-asymptotic approximations and new high-dimensional central limit theorems for the MinMax of the components of random matrices. Unlike the previous literature on functional inference in partially identified models, our results do not rely on weak convergence results based on Donsker's class assumptions and, in fact, our test statistic may not even converge in distribution. Our bootstrap approximation requires the choice of a tuning parameter sequence that can avoid the excessive concentration of our test statistic. To this end, we propose an asymptotically valid data-driven method to select this tuning parameter sequence. This method generalizes the selection of tuning parameter sequences to problems outside the Donsker's class assumptions and may also be of independent interest. Our procedures based on self-normalized moderate deviation bounds are relatively more conservative but easier to implement.