Simple subvector inference on sharp identified set in affine models
仿射模型中尖锐识别集的简易子向量推断AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要主要研究一般仿射矩条件下的部分识别与凸优化；区间结果变量的工具变量例子不足以确定所列具体应用方向。
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仿射模型中尖锐识别集的简易子向量推断
- 研究问题
- 参数由仿射矩等式与不等式部分识别时，如何对单个分量的尖锐界限进行统一有效、计算可行的统计推断？
- 方法与思路
- 作者构造正则化支撑函数估计量，并通过少量线性与凸二次规划计算分量置信集，同时讨论多分量及交集界限扩展。
- 材料陈述的贡献
- 摘要称估计量在所述几何条件下具有统一高斯极限，正则化偏差不进入一阶分布，且非正则情形仍保持尖锐集一致性。
- 阅读关注点
- 应核对平坦面与冗余约束的具体条件、正则化参数选择，以及非正则情形的一致性与统一推断结论各自覆盖的范围。
- 阅读边界
- 仅据所给出版社摘要，不能将统一高斯结论推广至任意约束几何；计算收益、覆盖率和具体调参规则尚需全文核对。
原文摘要
This paper studies a regularized support function estimator for bounds on components of the parameter vector in the case in which the identified set is a polygon. The proposed regularized estimator has three important properties: (i) it has a uniform asymptotic Gaussian limit in the presence of flat faces in the absence of redundant (or overidentifying) constraints (or vice versa); (ii) the bias from regularization does not enter the first-order limiting distribution; (iii) the estimator remains consistent for sharp (non-enlarged) identified set for the individual components even in the non-regular case. These properties are used to construct uniformly valid confidence sets for an element θ1 of a parameter vector θ∈Rd that is partially identified by affine moment equality and inequality conditions. The proposed confidence sets can be computed as a solution to a small number of linear and convex quadratic programs, leading to a substantial decrease in computation time and guarantees a global optimum. As a result, the method provides a uniformly valid inference in applications in which the dimension of the parameter space, d, and the number of inequalities, k, were previously computationally unfeasible (d,k=100). The proposed approach can be extended to construct confidence sets for intersection bounds, to construct joint polygon-shaped confidence sets for multiple components of θ, and to find the set of solutions to a linear program. Inference for coefficients in the linear IV regression model with an interval outcome is used as an illustrative example.